single word requests - what do you call a person who doesn't believe what another says anymore because that person is always lying?

There are a number of possibilities.

Dismissive describes your reaction to his statements.

Incredulous "unwilling or unable to believe something" is a good start, but the lack of belief could be caused by any number of reasons.

Profoundly mistrusting would describe your mental state, although it is two words rather than one.

Disillusioned does not precisely state that you do not believe the person, but it is pretty well implied.