On the twenty-seventh of May 1977 Marcel Lefebvre publicly announced that Liénart (The man who ordained and consecrated him) was a Freemason. He then assured us that despite this fact there is no reason to doubt the validity of his (Lefebvre's) ordination and subsequent consecration. As far as I know this much has not been disputed.
Also I think it fair to note that Lefebvre's doctrinal and perhaps moral integrity has been called into question by his own spiritual children (at least some of those ordained by him). Consider the spiritual ramifications of the doubtful validity of the ordination with the new rite of Philip Stark which is sited in: "The Nine vs. Lefebvre: We Resist You to Your Face" 2008 by Anthony Cekada. Cekada seems to make clear that Lefebvre was more interested in Novus Ordo politics than in the validity of the sacraments. By allowing a doubtful priest to function under him and administer "sacraments", Lefebvre exposed the people (who trusted him) to potential idolatry, invalid confessions, invalid Communions, etc. This I think speaks volumes of the lack of concern that Lefebvre had for doctrine and morals, not to mention the eternal salvation of souls.
Thus with Lefebvre's own honesty and theological integrity called into question (Not by me but, by his own former associates whom I assume vowed to obey him when they placed their hands in his at their "ordination") I do not feel out of line in questioning his theological conclusion concerning the certainty of Holy Orders administered by a known Freemason.
According to "The Catholic" No. 8, Aug 1987, Father John Martinez tells us that Achille Liénart was "ordained" a priest in 1907 and that he became a Freemason in 1912. About 1918 he entered the 18th degree of Freemasonry. By 1924 he had already reached the 30th degree of Freemasonry. He was "consecrated" a bishop in 1928.
According to the "Angelus" (July 1988 Vol XI No 7) Lefebvre was "ordained" 1929 Sept 21 by Liénart, and was "consecrated" 1947 Sept 18 by the same Liénart. Please note that Liénart was a 30th degree Freemason since at least 1924 and that Lefebvre's Ordination was therefore at least four years after he had reached this degree. Also, please keep in mind Lefebvre's lack of concern for validity of Holy Orders as noted above.
This far, I can see no reason to question these facts unless we either deny that Lefebvre made the public statement, or that Lefebvre was mistaken in what he said about a man who both "ordained" and "consecrated" him, or perhaps that Lefebvre is an outright liar and made the whole story up. As the public statement is undeniable, that leaves us with either of the other two options -- neither of which is very flattering for him.
The only question now is the sacramental ramification of having a Masonic "bishop" "ordaining". Is such an "ordination" valid? (I don't think anyone would deny that it is illicit for an excommunicated person to confer the sacraments.) The proponents for the validity of the Sacrament propose that no formal declaration has ever been passed by the Church stating that such situations are invalid. They likewise propose that Talleyrand was acknowledged as having passed on valid orders as a Freemason. Though Talleyrand lived an immoral life and sided with the French revolution, I can find no indication of membership in a Masonic lodge, much less to the high degree that Liénart reached. He was a fallen clergyman who was weak in his faith to the point of cowardice, and took advantage of the opportunities of the day to indulge his passions and vices. His immorality and vices are not questioned, but this is not the point at issue. (Unless they wish us to conclude that Liénart also led a dissolute life which has never been my claim.) For this case of Talleyrand to have any import it must be shown that he was a high ranking Freemason, which has not been done.
So the argument concerning Talleyrand does not prove their point. Likewise, just because we can find no precedent of specific examples of the validity or invalidity of sacraments administered by Freemasons proves nothing one way or the other. It only proves that we have not yet found one or the situation has not been specifically dealt with.
So what are we left to do? We must refer to principles of sacramental and doctrinal theology and aided by reason draw forth logical conclusions.
Let us examine what the Church has to say concerning Freemasonry. There are many popes and encyclicals dealing with this topic, not to mention the Canon Law of the Church which forbids membership in the Freemasons under penalty of excommunication.
We must acknowledge with Pope Leo XIII in "Humanum Genus" that: "There may be persons amongst these, and not a few who, although not free from the guilt of having entangled themselves in such association, yet are neither themselves partners in their criminal acts nor aware of the ultimate object which they are endeavoring to attain." Freemasonry by its very nature of secrecy and degrees allows for countless numbers (in the lower degrees) to enter and commit themselves to evils that they are as yet unaware of. Such people while they are guilty for their indifference or carelessness cannot be completely culpable for the actions that they do not knowingly, willingly, and freely commit. But, we are not dealing with someone in these lower degrees. Remember that Liénart was a 30th degree Freemason at the time that he "ordained" Lefebvre, and this is one of the higher ranks.
So we are not dealing with someone who is ignorant that he is excommunicated from the Church ipso-facto by Canon Law, or one who is ignorant of the intentions of this Satanic religion. Let us just consider some of the oaths that this person had taken in the Masonic Lodge in order to reach this level. The following is taken from the Catholic Encyclopedia 1910 under the heading of "Masonry":
In view of the fact that the secrets of Masonry are unknown to the bulk of Masons, the oaths of secrecy taken on the Bible are all the more startling and unjustifiable. The oath, for instance, of the first degree is as follows: "I, in the presence of the Great Architect of the Universe, . . . do hereby and hereon solemnly and sincerely swear , that I will always hide, conceal and never reveal any part or parts, any point or points of the secrets or mysteries of or belonging to Free and Accepted Masons in Masonry which may heretofore have been known by, shall now or may at any future time be communicated to me" etc. "These several points I solemnly swear to observe under no less penalty, than to have my throat cut across, my tongue torn out by the root and my body buried in the sands of the sea", "or the more efficient punishment of being branded as a willfully perjured individual, void of all moral worth". "So help me God", etc.
Similar oaths, but with severer penalties attached, are taken in the advanced degrees. The principle contents of the promises are according to Pike:
Eighteenth degree: "I obligate and pledge myself always to sustain, that it belongs to Masonry to teach the great unsectarian truths, that do not exclusively belong to any religion and acknowledge that I have no right whatever to exact from others the acceptation of any particular interpretation of masonic symbols, that I may attribute to them by the virtue of my personal belief. I obligate and solemnly pledge myself to respect and sustain by all means and under any circumstances Liberty of Speech, Liberty of Thought and Liberty of Conscience in religious and political matters". 
Thirtieth Degree: A. - "I solemnly and freely vow obedience to all the laws and regulations of the Order, whose belief will be my belief, I promise obedience to all my regular superiors. . . . I pledge myself to be devoted, soul and body, to the protection of innocence, the vindication of right, the crushing of oppression and the punishment of every infraction against the law of Humanity and of Man's rights . . . never, either by interest or by fear, or even to save my existence, to submit to nor suffer any material despotism, that may enslave or oppress humanity by the usurpation or abuse of power. I vow never to submit to or tolerate any intellectual Despotism, that may pretend to chain or fetter free thought, etc."
B. "I solemnly vow to consecrate my life to the ends of the Order of Knights of Kadosh, and to co-operate most efficaciously by all means prescribed by the constituted authorities of the order to attain them. I solemnly vow and consecrate, to these ends, my words, my power, my strength, my influence, my intelligence and my life. I vow to consider myself henceforward and forever as the Apostle of Truth and of the rights of man."
C. "I vow myself to the utmost to bring due punishment upon the oppressors, the usurpers and the wicked; I pledge myself never to harm a Knight Kadosh, either by word or deed . . .; I vow that if I find him as a foe in the battlefield, I will save his life, when he makes me the Sign of Distress, and that I will free him from prison and confinement upon land or water, even to the risk of my own life or my own liberty. I pledge myself to vindicate right and truth even by might and violence, if necessary and duly ordered by my regular superiors."
D. "I pledge myself to obey without hesitation any order whatever it may be of my regular Superiors in the Order". 
This thirtieth degree is also known as the "Order of Knights of Kadosh" as seen above. In this same article from the Catholic Encyclopedia we read about this order:
The Kadosh (thirtieth degree), trampling on the papal tiara and the royal crown, is destined to wreak a just vengeance on these "high criminals" for the murder of Molay  and "as the apostle of truth and the rights of man"  to deliver mankind "from the bondage of Despotism and the thraldom of spiritual Tyranny".  "In most rituals of this degree everything breathes vengeance" against religious and political "Despotism".
We see clearly that those, at least in the thirtieth degree, have sworn to do all in their power to undermine and destroy the Church. Pope Leo XIII in "Humanum Genus" shows us that ". . . and now the time has come when the partisans of the sects openly declare, what in secret among themselves they have for a long time plotted, that the sacred power of the Pontiffs must be abolished, and that the papacy itself, founded by divine right must be utterly destroyed. If other proofs were wanting, this fact would be sufficiently disclosed by the testimony of men well informed, of whom some at other times, and others again recently, have declared it to be true of the Freemasons that they especially desire to assail the Church with irreconcilable hostility, and that they will never rest until they have destroyed whatever the supreme Pontiffs have established for the sake of religion."
This same pontiff, Leo XIII in "Custodi Di Quella Fede" says: "They encourage schisms, apostasies, and revolts against legitimate superiors in the Church. Religious vows and especially religious obedience are rebuked as contrary to human dignity and freedom, while impious associations which bind their followers by wicked oaths and demand blind, absolute obedience in crime are allowed to flourish with impunity."
I think therefore that any honest person, who has taken the time to read what the Popes have said concerning Freemasonry or have even just read the article on Masonry from the Catholic Encyclopedia, must conclude that Freemasonry and the Catholic faith are diametrically opposite. A Catholic cannot be a Freemason nor can a Freemason be a Catholic. Again let me give a quote from the Catholic Encyclopedia: "Past Grand Deacon J.C. Parkinson, an illustrious English Mason, frankly avows: 'The two systems of Romanism and Freemasonry are not only incompatible, but they are radically opposed to each other'  and American Masons say: 'We won't make a man a Freemason, until we know that he isn't a Catholic.'"
So far, I have established that Lefebvre was "ordained" by Liénart and that Liénart was a thirtieth degree Freemason prior to this "ordination". Such a Freemason (as Liénart was at that time) has previously vowed his hatred for the Church and not only this but he is "radically opposed" to the Church.
We know from theology that the minister of ordination must have the minimum intention of doing what the Church does. We know from the above that Liénart has the opposite intention as manifested by his rank of thirtieth degree Masonic Knight of Kadosh.
Now the proponents for the validity of the "ordination" will tell us that Theology teaches us that when the external ceremonies are performed we must assume that the intention is likewise present and that it is in accord with the actions performed. But they fail to grasp the rest of the teaching: "unless there is evidence to the contrary". So the question now is: Is there evidence to the contrary? Can it be said that despite everything externally being in order (which we have not verified) that not everything was intentionally in order? The evidence of membership in the Order of Kadosh, I think is such evidence to the contrary.
We know that "Every validly consecrated bishop, including heretical, schismatic, simonistic or exommunicated bishops, can validly dispense the Sacrament of Order, provided that he has the requisite intention, and follows the essential external rite (sent. Certa)." (Fundamentals of Catholic Dogma by Dr. Ludwig Ott)
Assuming that Liénart was a valid bishop (Which is doubtful as he was a high ranking Mason before his "consecration". He was 30th degree before 1924; "consecrated" 1928) then, we see from Ott that he "can validly dispense the Sacrament of Order, provided that he has the requisite intention," etc. But, being able to do something and doing it are not the same. Just because he "can" does not mean that he "does".
In "Principles of Sacramental Theology" by Bernard Leeming, S.J. we read: "552. . . if in fact the minister resolves not to do what the Church does, he has not sufficient intention and the sacrament is invalid: this was categorically affirmed about Baptism by Alexander VIII in 1690. About Orders, it was affirmed by the Congregation of the Council, in the cases of bishops not intending to ordain a particular class of candidates. . . Thus the mind of the Church is clear that it is possible for a minister to have the intention of not doing what the Church does, and that if such is the case, the sacrament is invalid. This teaching is universally accepted by modern theologians, who agree that a sacrament is invalidated even by a secret intention of the minister contrary to the substantial nature of the sacrament."
"On 23 January, 1586, the Sacred Congregation of the Council gave a decision in the following cases: A Bishop, before the Ordination ceremony, declared that he had no intention of ordaining any candidates who were under age, and that if any such received the imposition of hands, it would be an empty ceremony. The answer was that those under age were not ordained."
"A certain Anthony Gonzalez de Acuna, Bishop of Charcas in South America, declared with an oath before an ordination ceremony that he intended not to confer orders on any candidate of mixed blood. Several such presented themselves and received the rite at his hands. The case was referred to Rome, and on 13 February, 1682, the Sacred Congregation of the Council, which while gravely rebuking the Bishop for his conduct, pronounced that the Orders were invalid in the case of those of mixed blood, and that all priestly acts performed by them were invalid."
Allow me to quote once again from the Catholic Encyclopedia concerning the goals of Masonry: "To destroy radically by open persecution of the Church or by a hypocritical fraudulent system of separation between State and Church, all social influence of the Church and of religion, insidiously called "clericalism", and, as far as possible, to destroy the Church and all true, i.e., superhuman religion, which is more than a vague cult of fatherland and of humanity."
This appears to be self-evidently incompatible with the goal of the Church in ordaining.
It is not necessary to show that in fact Liénart withheld the intention to ordain. I do not dispute that if he was a true bishop he could have had the correct intention. I simply present the fact that it is doubtful that a man who vows his hatred for the Church and his determination to do all in his power to undermine Her, actually does have the opposite intention of doing what the Church does. In this case where a man presents two opposing intentions we have been given a positive reason to doubt his intention. Either he is lying as a Mason or lying as a Catholic. In either case he is a proven liar and his intentions must be questioned. There is no longer any reason to presume that the intention to ordain is there simply because the ceremony was performed. There is a legitimate reason to doubt.
In the case of such positive doubt one must take the safer course and the doubtful priest must be treated as a non-priest until the doubt is removed or he is ordained either outright or conditionally. This course is taken because the other option would expose souls to doubtful sacraments because the minister is doubtfully a priest.
Therefore: 1) Liénart was a 30th degree Freemason, who doubtfully ordained and doubtfully consecrated Lefebvre. 2) Lefebvre is doubtfully a priest and bishop. 3) All those "ordained" by Lefebvre are doubtfully ordained. 4) All "Orders" stemming from Liénart-Lefebvre are at best doubtful and must be treated as invalid.
It is for the love of God and the salvation of souls that I hold this position. It is not out of malice or ill will toward anyone, but because these are the simple facts set before any and all objective truth seekers.
"God forbid that I should glory save in the cross of our Lord Jesus Christ, through whom the world is crucified to me, and I to the world." (Gal. 6: 14)