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Stubborn, SPelli is correct about the Ordinary and Universal Magisterium. Read Footnote #40 in the Lumen Gentium quote that you provided.

Here is your original quote from Lumen Gentium again:

Although the individual bishops do not enjoy the prerogative of infallibility, they nevertheless proclaim Christ's doctrine infallibly whenever, even though dispersed through the world, but still maintaining the bond of communion among themselves and with the successor of Peter, and authentically teaching matters of faith and morals, they are in agreement on one position as definitively to be held.(40*) This is even more clearly verified when, gathered together in an ecuмenical council, they are teachers and judges of faith and morals for the universal Church, whose definitions must be adhered to with the submission of faith.(41*)

Here is the text of Footnote 40 in Lumen Gentium:

Explained in my previous post.

At any rate, to post it again....

For us, we know that after Pentecost, at the decent of the Holy Ghost upon Our Blessed Mother and the Apostles is when St. Peter and all the Apostles were made individually infallible. God did this in order to establish and facilitate the beginnings of the Church throughout the entire world.

This being the case, whatever each of the Apostles, individually dispersed as they were  throughout the world taught regarding the faith, by virtue of the descent of the Holy Ghost at Pentecost, were most certainly:
1) each individually infallible, and on that account,
2) whatever they taught regarding the faith, they would have all taught the exact same thing in unison, as such,
3) no matter what they taught regarding the faith, because they all taught infallible truth, they would have all been in agreement with each other and St. Peter - not to mention with all the future popes whenever they speak ex cathedra till the end of time.

That's infallibility, that's how infallibility works, that's how infallibility worked when the Church on earth was in it's infancy. Our Pentecost's foundation is where the Church's infallibility was born and built on infallible truth which can never change whether dispersed throughout the world or all together.

OTOH, the NO's Second Pentecost's idea of infallibility is built upon the idea that, "truth is what we say it is", it's "the unanimous agreement of the totality of bishops in union with the pope that makes teachings infallible", which as we have seen for the last 60 years, is entirely and utterly false.

It is at V2 where even the very definition of "infallible" took on a new meaning - this new meaning is inherent in the NO doctrine of LG 25.2. This is because since V2, it means whatever the pope and bishops teach regarding the new religion is infallible, it therefore means whatever was taught by whomever prior to V2 is really nothing more than yesterdays headlines and a memory they strive to erase (except when they want to pull this or that out as a reference to show they're in line with tradition).

No, it doesn't consider non-Catholic groups to be particular Churches.  It considers particular Churches to be/remain particular Churches even if they are presently occupied by an orthodox bishop not in union with the Pope.

Do you know what a particular Church is?  A particular church is a lawfully established see, either an Apostolic see (one founded by an Apostles) or an episcopal see (one legally established by a subsequent Pope), with rights, duties and privileges attached to it, to be enjoyed by the bishop who is appointed as its head.  The universal church is made up of thousands of particular Churches.  They exist in the universal Church and the universal Church exists in them.

When a bishop dies, and his see falls vacant, the particular Church itself continues to exist as part of the universal Church, waiting for its new head to be appointed.  If, for some reason, a non-Catholic "bishop" was illegally appointed as its head, the particular Church itself would continue to exist (with the rights, duties and privileges attached to it), while awaiting a new legally appointed head to be appointed.

Now, the Orthodox have particular churches. Some were founded by an Apostles and others were legally established by a Pope.  The problem is that the bishop who heads them is not in union with Rome and was probably (this is where it gets tricky) not legally appointed.

But a lawfully established particular Church does not cease to be part of the universal Church simply because it has been usurped.  It remains a particular Church that belongs, by legal right, to the universal Church that legally established it.

So, although you didn't quote Vatican II, what it probably teaches is that the orthodox have particular Churches, which is true, and not that it "considers non-Catholic groups to be particular Churches."  No Protestant sect or Anglican sect is a particular Church, and any episcopal see that the orthodox have, which was not lawfully established by the Catholic Church, is not a true particular Church.

Correct again. Much of the railing against the Vatican II docuмents is simply over-zealous misunderstanding. The real problem with the official docuмents of VII is the intentional ambiguity found in certain phrases therein. And by definition if that phrasing is "ambiguous" it can be interpreted in both good and bad ways. And as Benedict XVI tried to explain, these ambiguities should be interpreted using a "hermeneutic of continuity" to avoid the misunderstandings.

All of the players, the Sedes, the SSPX, and the modernist destroyers use the wrong hermeneutic, the "hermeneutic of rupture," to interpret the meaning of those ambiguous phrases. The Sedes conclude that the Popes "defected" by teaching heresy, not understanding the precise definition of "heresy." The SSPX concludes that the Popes "defected" in some sense but "no one can judge the Pope," so they just "recognize and resist" him. And the modernists use their interpretation of VII to justify their propaganda and carry out their destructive goals.

The only sane view is the one that is constantly ignored: that the Vatican II docuмents were not precisely "heretical" because it is impossible to pin down a precise meaning for the ambiguities that cause the problem. An ambiguity is not a "heresy."

Having said all of that, there are many bad things that Church authorities (especially national conferences of bishops) have done since Vatican II, claiming falsely that Vatican II authorizes those things. And the Sedes and SSPX are correct to fight against that. None of the Popes since VII were able to stop the modernist demolition of the Church (if they even tried). But Bergoglio is not one of them, because he's not a canonically-elected Pope. He is simply a usurper of the papacy and a heretic. He is "the eighth and is of the seven [kings], and goeth into destruction" (Apoc. 17:11).

Catholics of good will need to stop fighting each other and fight the real enemy: Antichrist Bergoglio.