At least you have to say for what the Bible says about Lot that he was troubled, vexed, tormented, tortured by what was going on around him, even though he chose unwisely, foolishly to live within it. So Lot appears to have had a measure of faith, but his approach to living was quite a bit different from Abraham's.
So Lot left Egypt, but apparently Egypt never left Lot. It shows he was an upright man, a good man. He was a great deal like the Israelites who came out of Egypt. The fact that he chose to go in that direction toward Sodom and Gomorrah rather than resolving the problem that arose between his herdsmen and the herdsmen of Abraham, and instead choosing the ground that was like Egypt, or rather than return to Abraham and allowing him to make the choice, shows us a very great deal about Lot and his approach to life.
Does it not appear to you that he was a man of some faith, and at least intellectually, he wanted to follow the ways of God, but he wanted to do it with one foot in the world. He was not like Abraham. He consciously chose to separate himself from within the context of what was being worked out at that time.
Things today are a little bit different than they were in Abraham’s day, that is, what God is working out. God is teaching us something here. The man of true faith separates himself as far as he can possibly get from the world. The person whose faith is weak, though he does have some faith, gets as close to the edge of the cliff as he possibly can get, but still tries to somehow keep God [unclear]. Now Lot seems to have compensated and in some way justified what he was doing in Sodom by preaching to these people and scolding them for their sins. But he never entirely broke away from that way of life himself.