I knew someone who had been diagnosed with anti-social personality disorder. From what I have read about the associated behaviors and symptoms, this makes sense as a diagnosis for him.
My question is this: when a person with this disorder accuses friends, family, etc. of stealing from him, lying to him, and so on, without any evidence to support his claims, is it more likely that he believes it to be true, or that he knows he is not correct, and has convinced himself that accusing people of these things is somehow justified and/or necessary? Since he is a very effective liar, I truly wasn’t able to tell.

He firmly believes it is true even when evidence to the contrary is presented to him.

It doesn't matter what mental issues he is diagnosed with by his doctors. You have probably seen enough of his words, actions and behavior to formulate your own plan of how you deal with this individual. If you cannot tell whether he is honest or real or just a drama queen NUT, then best keep a safe distance from any BS he may be involved in be it real or imagined.

That's not easy if you genuinely like the person, he may treat you well, but you don't have to take his side, or word for anything he says when it comes to your words, or actions concerning matters he is involved in, or the other people caught in his BS. Just being to close to people with issues makes you a target by association of others he has gotten on the wrong side of as I bet he poisons your opinion of them to separate you from them and keep you on his side against them.

If that's the case be aware of his manipulations, and protect your own reputation. Yes I would certainly keep my distance just for my own good.