When Lot's father Haran died in Ur of Chaldeans, Lot joined with Abraham in a series of family migrations. First, from Ur to Haran, where Terah died (Genesis 11:28-32). It was in Haran that The Lord (see Rock Of Ages) appeared to Abram (before He renamed him Abraham), and told him to go to the land of Canaan (Genesis 12:1-4). The stepping-stone movements continued from Bethel (Genesis 12:8), to the Negev (Genesis 12:9), to Egypt to escape a famine (Genesis 12:10), then back to the Negev (Genesis 13:1), and once again to Bethel (Genesis 13:3). See Bible Places.
It was in Bethel that the split between Abraham and Lot occurred in a dispute over grazing their flocks (Genesis 13:3-13). Given the opportunity to go either direction, Lot made a fateful choice - to the east, near the then-infamous city of Sodom (Genesis 13:10-13). It's destruction, and how Lot survived it, is covered in Remember Lot's Wife and The Destruction Of Sodom.
An incident just before the destruction of Sodom has caused many to look at Lot with revulsion - his offering of his two young daughters to the evil mob:
"Look, I have two daughters who have never slept with a man. Let me bring them out to you, and you can do what you like with them. But don't do anything to these men, for they have come under the protection of my roof." (Genesis 19:8)
Did Lot really mean it? Would he really have handed his two daughters over to the mob? Or, was it intended as some sort of a diversionary tactic, an offer that would not be accepted, because he knew that those men had no interest in women? That could be a possibility to consider, in view of the mob's response - they continued to ignore the two daughters, and decided to assault Lot along with the two men/angels. (Genesis 19:9)
After their escape from Sodom, Lot and his two daughters took refuge in a cave. It was there that another controversial chapter in Lot's life occurred, although the record states that he was an unknowing participant:
"Lot and his two daughters left Zoar and settled in the mountains, for he was afraid to stay in Zoar. He and his two daughters lived in a cave. One day the older daughter said to the younger, "Our father is old, and there is no man around here to lie with us, as is the custom all over the earth. Let's get our father to drink wine and then lie with him and preserve our family line through our father." That night they got their father to drink wine, and the older daughter went in and lay with him. He was not aware of it when she lay down or when she got up. The next day the older daughter said to the younger, "Last night I lay with my father. Let's get him to drink wine again tonight, and you go in and lie with him so we can preserve our family line through our father." So they got their father to drink wine that night also, and the younger daughter went and lay with him. Again he was not aware of it when she lay down or when she got up. So both of Lot's daughters became pregnant by their father. The older daughter had a son, and she named him Moab; he is the father of the Moabites of today. The younger daughter also had a son, and she named him Ben-Ammi; he is the father of the Ammonites of today." (Genesis 19:30-38)
Fact Finder: What did Peter have to say about Lot?
2 Peter 2:4-10