You have said that Lot was removed from Sodom because God wouldn’t judge the righteous with the wicked. In 2 Peter 2:7-8 Peter Peter also called Lot righteous. Why did Peter call him that?
Abraham’s unspoken question in his negotiations with the Lord concerning the destruction of Sodom (Genesis 18:16-33) was, “What about my nephew Lot?” He finally got the Lord to agree that if there were 10 righteous people there He would spare the city . The fact that He destroyed Sodom means there weren’t 10 righteous people there. But requiring the angels to remove Lot and his family before doing so (Genesis 19:22) means the Lord considered Lot to be a righteous person. If the Lord felt that way about Lot, it explains why Peter did as well.
Lot is a good example of the Lord judging us by the motives of our heart. In the case of his two daughters the Bible states very clearly that Lot was not aware of either daughter using him to impregnate themselves (Genesis 19:31-35). Obviously he knew what had happened soon enough, but it was only after the fact. As far as the Lord was concerned, Lot’s righteousness remained intact.