Does anyone do this? Are we allowed to bring a recorder and... well record the lecture? Do many lecturers allow this?
It depends on the subject and the teacher.
As a general rule - unless in the 1st introductory lecture, the lecturer says you can, ask them permission.
Also, check your unit outline as for example, I have one unit this semester and one next semester that expressly prohibit any form of recording of the class.
I wouldn't recommended any form video recording as you're likely to get a no for that, and apart from anything else, you only really need the audio. You may find though, especially if you're doing a business degree, you'll end up doing what I and other friends did - you record the lectures, but never end up listening to them so you stop recording stuff after 1st semester lol