I used to have a friend who frequently lied. At first we all thought if we were gentle with him, he would grow out of it. Instead he got worse. When he started telling lies designed to turn me against my brother, that was when I knew it was time to kick him to the curb.
Or alternatively, I have heard of an associate of a friend who is a compulsive liar. Basically they used their contact with this person purely to laugh at the whoppers he would unabashedly drop and not realize that what they were saying was completely ridiculous.
So how you deal with this person is entirely up to you, but I would caution that anyone who would intentionally mislead you is someone who disrespects you at a fundamental level. The moment they started lying to you, they stopped being your friend. You don't owe them any friendship in return. I say maintain the relationship only as long as you get something out of it. But beware that allowing a liar to get away with their lies can be a form of enabling. Sometimes we don't need understanding to overcome our problems. Sometimes we need nothing more than a sharp kick in the ass.