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As you point out, Cera, this Litany is so absurd that it must be a spoof.

How I wish that were true. I found this commentary on the “Litany” to Plinio’s mother. . .
The most extraordinary claim here is also the most obscure, "Mother of the Axiological Principle": this means a principle requiring no previous principle, in other words God himself.

This hymn came into public domain when it was revealed by Prof. Orlando Fedeli, a member of TFP for over 30 years, who asked Mons. Antonio de Castro Mayer for his opinion on its orthodoxy. One can see where the roots of Introvigne's dislike for "apostates" lies. TFP did not deny the allegation; it simply shifted the blame on over-zealous young followers, and claimed the hymn to be perfectly orthodox ((Carlo Alberto Agnoli e Paolo Taufer, TFP: la maschera e il volto, Ed. Adveniat, S.Giustina di Rimini, s.d., p. 17 ss). - shifting the blame onto the boys is a time-honoured practice in certain kinds of organizations. It also claimed that use of the hymn had long been discontinued. The current official version of this issue is given by Roberto de Mattei in his hagiography of Doctor Plinio (Roberto de Mattei, Il crociato del secolo XX: Plinio Corrêa de Oliveira, Piemme, Casale Monferrato, 1996, p. 249): 

"It is true that for a certain period some co-operators of the association used a litany with invocations to Lady Lucilia, composed by two adolescents late in 1977. This litany was forbidden by Prof. Corrêa de Oliveira as soon as he got word of it"

Oddly, this hymn by Brazilian adolescents seems to have spread across the ocean, since it was certainly used in France in the early '80s, and a former AC member recently told me that some TFP affiliates were still using it in Italy in the early '90s. When nothing else works, shocked TFP sympathizers who discover this hymn are told that "things are different in Latin America": this happened to be a favourite stratagem in my group, New Acropolis, which came from Latin America too.

If Plinio's mother is the Virgin Lucilia, her offspring of course must be quite special. Just how special appears from an extraordinary episode, which can hardly be blamed on over-zealous adolescents, since it is based on a statement made by Plinio, repeated in many works on him, and - as usual - proudly narrated in Cristianità. ("In memoriam: Plinio Corrêa de Oliveira", November-December 1995, p. 6):

"On February 1st, 1975, in view of the increasingly difficult situation of the Catholic Church, and hence of the Catholic world, during a meeting of the Brazilian TFP, he offered himself as an expiatory victim. Thirty-six hours later he was seriously wounded in a car accident, the consequences of which followed him until his death"

More than its political character, it was this highly suspect theological nature of the group which led to its condemnation by the Council of Brazilian bishop

"During its 23rd plenary assembly, the Council of Brazilian bishops approved a note concerning the 'Brazilian Society for the Defence of Tradition, Family and Property', advising Catholics not to join the above mentioned Society […]. Its esoteric character, its religious fanaticism, the personality cult of the founder and of his mother, the abuse of the name of the Virgin Mary […] can absolutely not be approved of by the Church" 
 
(Osservatore Romano, July 7, 1985, p. 12, n. 408, weekly Spanish edition quoted in Tradizione Famiglia Proprietà: Associazione cattolica o setta millenarista?, Rimini 1996, frontispiece)
 
The terms "cult" or "sect", with their double meaning of "deviant religious behaviour compared to an institutional religion" and a "closed totalist group", are certainly ambiguous. But this condemnation of TFP reveals why the organization was certainly considered by some to be a "cult" in the first sense of the word; and why therefore this organization took a special interest in the issue of "cults" in 1985, that is exactly when Introvigne too started involving himself in this matter.

Former TFP members have written that Plinio was well aware of this association. Referring to cult accusations, he used to tell them:

"This must not come as a surprise; since you belong to TFP, you will be treated as if you belonged to a cult, by your very parents and friends! It will be terrible, and it will be hard indeed to stay faithful."
 
(Tradizione Famiglia Proprietà: Associazione cattolica o setta millenarista?, Rimini 1996, p. 38)

https://mond.at/kelebek/cesnur/storia/gb14.htm

Hah, I called it.  These two kids were undoubtedly rolling on the ground with side-splitting laughter as people read this thing.  Prof. de Oliveira banned it ... having recognized it for what it was.

After I had become a Traditional Catholic, my younger brother was still at a Novus Ordo grade school.  My brothers and I sat down and brainstormed a satirical parody of the Novus Ordo in an essay he was to submit for a high school scholarship.  We were rolling with laughter, and tears running down our cheeks, as we filled this thing with one satirical use of Novus Ordo cliche after another.  To our complete shock, he won the scholarship ... as the judges took the thing seriously and didn't see through the satire.  We also authored something called, "The Community Poem" ... with which we had a lot of fun.  These two kids were obviously doing the same thing with this Litany.  Now, if one or another pocket of TFP folks took this thing seriously, then the kids were laughing even harder about that.  They were obviously mocking Plinio and his Mother with this production ... an obvious parody of some things that the Professor was teaching.

Like you, I would love to believe that. But how to explain that its use spread to Europe in the 80s and 90s?
Also, how to explain this:
Dr. Plinio often prophesied that he would see the battle of Armageddon within his own lifetime. His followers were kept in a constant state of agitation, expecting this cataclysmic event at any moment. The warrior monks are supposed to be key participants in Armageddon and the subsequent “Reign of Mary”. This false prophet was treated a “living saint”; his followers would bow in his presence, revere his personal belongings and compose hymns honoring him and his mother. Some militants chant a litany to Donna Lucilla, Dr. Plinio’s deceased mother, or substitute the name of Donna Lucilla for Mary and the name of Plinio for Jesus while reciting the Hail Mary.

https://ephesians511blog.com/2013/09/28/america-needs-fatima-a-cult-using-the-fatima-name/