TL;DR: Use books to learn.
Is that a course about some obscure topic? Is a book (or books) available with information about that course?
If a written material (book or lecture notes) for learning is not available
Ask your professor how could you study the subject on your own if you don't understand dully some of the topics. Tell that you have troubles taking notes of everything and that you are afraid of missing something or making mistakes in notes while you misendurstand the topic.
If the professor tells you that the are no valid books on this subject and the lectures is the only source, ask if you may record the lectures on your phone. Explain that you would use it only for your own learning and audio recordings of lectures help you in other courses because you can pause, rewind and go in your own tempo. It would be quite strange if this gets denied.
If there is a book or other written materials available
Don't record the lectures.
I am teaching myself. If a student would come up to me and ask to record the lectures, I would allow it but I would think to myself that the student is an idiot. To put a more objective term that I could use with students and colleagues, I would say that the student does not know how to learn.
I would allow it because I think your approach to learning is your own business, but I can judge you on that and I think that the approach is wrong.
If you learn on your own, you should always use a book. It's up to your tempo. You can rewind it or skip over whenever you want. It is more thorough, it includes illustrations and formulas from the blackboard and a lot more information than what was told in lecture (but you can choose if you take it all or maybe even less than in the lecture).
A book is usually read more times by more people than a lecture is listened to and thus it is better checked for errors. Professors can and will make mistakes in lectures. And it will be your fault and problem if you misunderstand something because the professor mistakenly mixed up a couple of words and didn't notice it.
I wouldn't care if you recorded my mistake and showed it to someone - mistakes can happen to anyone. But if you genuinly misunderstand a crucial topic and try to put the blame on my mistakes, I will still grade you according to your knowledge and not forgive you because you recorded a mistake. A professor is there to guide you through course, the learning is up to you yourself.
The lectures is an introduction to the topic and gives you the overall picture. It is completely natural if you get distracted or miss something in lectures. No one can remain totally attentive for 45 or 90 minutes. I've missed something in every lecture I've attended yet I've never had problems to actually learn the topics by myself using resources.