If a person who is known for lying says anything, I would proceed with caution.
I’m a poor judge of liars because I’m not one and tend to believe what people say. But if my trust in someone has been compromised, never mind exterminated, I’m not going to be very quick to forget.
However, I do see a gray area. A person who reschedules a lunch date claiming a migraine is not in the same class with, say, someone who accuses me of doing something that he himself did and I didn’t, or who makes up a false story in order to get me to give him money.