What does ‘lecture or format’ refer to

The passage below is from A History of the Index by Dennis Duncan.

While the focus of teaching in the monasteries was on quiet contemplation, in the schools and universities, where students were being trained for careers in religious or secular administration, new methods of teaching came to dominate. Disputation, the citing of authorities, the reading-out of commentaries (a format with a now-familiar name: the lecture): scholastic learning would favour external demonstration over inner revelation, intellectual agility over endless meditation. University readers would require new tools on the page, new ways of efficiently finding parcels of text – a word, a phrase – amidst the prose block.

In the passage above I have two questions.

First, the meaning of ‘commentary’. It has two different meanings, one of them is review or critique, and the other is annotation or exegesis.

I cannot decide which one is IT.

Second, what does ‘lecture’ refer to?

I thought out three possibilities as follows: One, commentaries. Two, the reading-out of commentaries. Three, the citing of authorities, the reading-out of commentaries, that is disputation.

I cannot decide which one is IT, either.

Thanks in advance.