Because of past conflicts, I don't believe my advisor will write me a good LOR for postdoc positions. What should I do?
Once it became clear that you were not going to follow your advisor's advice on important issues, it might have been better to switch advisors to one you could work with. Instead, you continued, in effect, without an advisor. The limited meeting time, slow e-mail response, and requiring you to draft the LOR all suggest to me an attitude of "Why waste my time giving advice that won't be taken anyway?".

You cannot be sure he is lying about having other people draft their own LOR unless you have talked with every person for whom he has ever sent one. He may feel he knows some students well enough to write an LOR from scratch, but needs a draft for others.

The best you can do at this point is to write what you consider to be a reasonable LOR and give it to your non-advisor.