To fully grasp why Lot married the woman he married we must first understand Lot.
G-d tells Abraham that He will destroy Sodom and Gomorrah. We read in chapter 19, that Lot shows the visitors (angels) hospitality. However, in Genesis 19:5, the Sodomites ask for the angels. They wished to desecrate them. Rather than expose the angels to homosexuality, Lot offers his daughters instead. It is good that he tries to protect them, but the willingness to surrender his daughters to brutal rape and the impact it would have for the rest of their lives only goes to show that Lot saw his daughters as property. Is it right to offer his daughters to save the lives of strangers? Would it be more appropriate to offer his own life or, try to escape altogether?
There are other instances, too. When G-d gave Abraham the land of Israel, Abraham took the smaller land to settle the dispute because family was important to him. It was essential to keep the peace between brothers. Lot, didn't see it quite like that and arrogantly took the much larger land and cattle as a prize. Lot even pitched his tent facing Sodom, the land of the sinners. He would eventually mingle with themtoo, residing in the filth. Later, Genesis Rabba states that Lot was captured because he foolishly settled in Sodom. After the destruction of Sodom, his daughters thought the world was going to end and had sex with him while he was unconscious.
In short, Lot, Abraham’s nephew, was corrupted. Where Lot sought riches, Abraham sought spirituality and to come closer to G-d. Indeed a Midrash and the Rambam state that Abraham discovered G-d. These are the characteristics of a G-dly man.
Lot's predicament led him to marry a selfish woman, like himself. Her fate was sealed when Lot’s wife turns into a pillar of salt in Genesis 19:26. Lot was spared. Perhaps it was because G-d wanted to give him another chance to act justly. And he did.
PS The Midrash Genesis says that Abraham was so holy that he perceived angels the way how others see regular human beings; but Lot, who was not so pious saw angels as angels. Yet others like the Rambam said that neither saw angels. It was a dream.