I would advise against trying to typeset lectures live, at least
for my courses. I structure my lectures as an abstract detective
work: start with a motivating problem or example, experiment with
it, distill the key ideas, formalize them into definitions, deduce
consequences (theorems, new problems). I expect my students to be
active participants at each step. Paper notes work well for this,
because they are both low overheard and sufficiently free-form.
From my experience, students that typeset or try to write overly
formal notes during class miss that crucial live narrative of my
lectures; that makes me sad because I spend a ton of effort in
this story-building.
I do think proper typesetting is a great idea afterwards, during
its own dedicated phase; it is like the report-building stage of
the detective work, where findings are revisited and structured so
the detective can reflect on the case, compare it with others and
have a reference for the future.
For anyone interested in my very opinionated patterns for latex
typesetting in Vim, I have a github page with vim templates [0] and
some demos at reddit [1].
[0] https://github.com/ykonstant1/dotfiles
[1] https://www.reddit.com/r/unixporn/comments/jtjol5/cinnamon_l...