Some history.
In Europe, printing with moveable type was introduced in the 15th century. Before that time, texts had to be copied out by hand and were therefore enormously expensive.
Photocopying was invented in 1932 and was refined in various ways in the decades that followed.
The internet and the world-wide web were introduced during the last quarter of the 20th century.
It follows that today I could just email my lecture notes for a course to all the students registered for that course.
So what, then, is the point of giving lectures?

Lectures are not about providing lecture notes.
I think this is why most students turn up to lectures, and to be honest there are lecturers for whom this is the point of giving lectures.
But as my brief history above shows, this is a pretty pointless exercise.
My experience is that student notes are littered with mistakes and misreadings by no means just their fault.
Lectures really are a poor way of providing detailed lecture notes.
Either there should be a recommended book that students can refer to or the lecturer can provide detailed notes themselves.
So what are lectures actually for? I think the key to answering this question is the following:

Learning stuff on your own is hard. Here, then, are a few of the ways in which lectures can help.

Pace.
The first role of the lecturer is to decide what should be in the course/module.
This depends on what the students are supposed to already know and what other things they are being taught.
Having decided on what should be included, the material then has to be divided up into teachable pieces.
This is of course is background work that the lecturer carries out on behalf of the student.
It sets the scene.
The lectures then roll out this material but this involves deciding on pace.
This is a bit like a trainer in sport deciding what you should do when and for how long.
If you try to learn on your own it is easy to try to do too much in one go.

Motivation.
To learn something new, you have to understand what that thing is for.
One of the key jobs of a lecture is to provide a perspective on a subject that helps you to understand it.
This might involve talking about the history of the subject or perhaps the applications but there aren't any restrictions on what might help.
Often, a lecturer can call on their previous experiences of teaching the subject: they have learnt what learners find hard and have developed strategies
to help smooth their path.

Learning in real time.
Both proofs and examples in mathematics are best understood when they are described step by step.
Seeing a proof revealed in front of your eyes can be the best way of beginning the process of understanding that proof.
Whereas, a proof on the page just sits there and you have to be the one to bring it to life by working through it.
Although not quite the same, seeing a play performed is a different experience from trying to read it on the page.
But once you have seen the play performed reading the play becomes much easier.

Taking notes. The role of taking notes is not to obtain a highly inaccurate version of the book but to help you concentrate and listen attentively.
Just sitting and listening might work for some, but if that's all you're doing it is very easy for your mind to wander.

Learning by watching.  How a mathematician talks about mathematics is something that cannot be conveyed by a book. I think this is an underestimated facet of lectures
because we tend to focus on the written word.

Getting started. A lecture is a beginning not and end. It serves to help orientate you in part of a subject but the point of university is that you will then work in your own time
to deepen your understanding of that material. Since lectures come in a sequence, you should work through the contents of one lecture before attending the next.

You are not alone.  Study can be a lonely business. Although, as Satre once said, `hell is other people', perhaps he was just having a bad day, it can be reassuring to know that other people
are finding material difficult. In particular, there should always be opportunities to ask questions in lectures. More to the point, a receptive lecturer will pick up from a class when they are having
difficulties. In addition, the pleasure of watching a lecturer make a mistake should never be underestimated.

Enthusiasm. At their best, lectures can help you see that a subject is interesting and encourage you to want to learn more about it. This is the ideal that we aim for.