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In this way the doctrine which the Ecumenical Council Vatican I had intended will be completed.... It is proper for this solemn Synod to settle certain laborious theological controversies about the shepherds of the Church, with the prerogatives which lawfully flow from the episcopate, and to pronounce a statement on them that is certain. We must declare what is the true notion of the hierarchical orders and to decide with authority and with a certainty which it will not be legitimate to call into doubt. (Paul VI, Opening speech to the Third Session)

This Sacred Council, following closely in the footsteps of the First Vatican Council...Continuing in that same undertaking, this Council is resolved to declare and proclaim before all men the doctrine concerning bishops, the successors of the apostles, who together with the successor of Peter, the Vicar of Christ,(2*) the visible Head of the whole Church, govern the house of the living God.
And the Sacred Council teaches that by episcopal consecration the fullness of the sacrament of Orders is conferred, that fullness of power, namely, which both in the Church's liturgical practice and in the language of the Fathers of the Church is called the high priesthood, the supreme power of the sacred ministry. ( Lumen Gentium )

This was clearly infallible. Lumen Gentium §25 says concerning the infallibility of a Council:

This is even more clearly verified when, gathered together in an ecumenical 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.

To understand what definition means, we can consult the meaning of the word defines from Pastor Aeternus:

Rather, the word 'defines' signifies that the Pope directly and conclusively pronounces his sentence about a doctrine which concerns matters of faith or morals and does so in such a way that each one of the faithful can be certain of the mind of the Apostolic See, of the mind of the Roman Pontiff; in such a way, indeed, that he or she knows for certain that such and such a doctrine is held to be heretical, proximate to heresy, certain or erroneous, etc., by the Roman Pontiff . Such, therefore, is the meaning of the word defines. (James T. O'Connor, The Gift of Infallibility: The Official Relatio on Infallibility of Bishop Vincent Gasser at Vatican Council I pp. 73-74)

Therefore Lumen Gentium §21 contains an infallible definition.

The first passage is from a speech by Paul VI asking the Council to settle long disputed issues regarding the role of bishops. It is speculative at best. In fact, when the Council in Lumen Gentium ended up exalting the role of the bishops and diminishing that of the papacy, Paul VI issued his famous Nota Praevia in which he reversed himself, saying nothing was to be made binding on the Church unless it was openly so stated. Nothing ever was.

The second passage is simply stating the obvious--that the bishops and the pope govern the Church. Nothing new here, nothing that hadn't been said before in a million different venues. The same goes for the following statement on Sacred Orders. This is old hat--issues settled in the earliest stages of the Church's history. And again, the statement regarding the infallibility of councils was also long-held Church doctrine.

The issue of how dogmatic statements are defined was interesting--because I have been saying this all along. (See some of my former posts on this thread.) The faithful must have certainty as to what was intended as a binding decree made by a pope or council. Ambiguity or lack of clarity cannot bind the intellect of anybody. This is so obvious it hardly needs mentioning. This is why it is incumbent upon pope or council to make its definitions with great clarity.