What I do in this situation, and I have had several especially in college, is ask yourself "if I happened upon this guy getting his ass kicked, would I step in and help him?"
There have been a few annoying people in my life but they were good-hearted so to speak and once I acknowledged that I would defend them if I found them in that situation, their annoyances became pretty muted.
If you wouldn't defend the guy, then tell him to leave you alone, or call him out on his lying every time he does until he stops or finds someone else to bother.