Well, I guess if you don't want his lying to bother you, you need to stop wanting to know whether he is lying or not.
What would happen if you just made a decision to believe everything he says and ACT as if it was true? Would that be comfortable for you? And if you later discover that he has in fact lied, you could say to yourself "Oh, that was one of those lies coming up. Bound to be a certain percentage of them, I guess!" Would that be comfortable for you?
Speaking of percentages, you could alternatively make up your mind to believe one in every four of his statements. So treat every fourth statement as a lie. Don't check whether it is or isn't. Just decide that his level of lying is one in every four, or one in every three, or whatever it is, and then arbitrarily believe the first three, and disbelieve the fourth one, without worrying about it. How would that feel?