The Quran says that Allah likes Lot (along with Ishmael, Elisha, and Jonah) better than all his others creatures (6:18).
It includes the story about him offering his daughters to the crowd of male Sodomites (11:78, 15:71), but not the one about him getting drunk and impregnating them.
In the Quran's story, Lot's wife remains in in Sodom and is destroyed with the Sodomites (29:32-33), and she (along with Noah's wife) is now is burnig in the fire of hell (66:10).
God rained fire and brimstone on Sodom and Gomorrah (v.24)
God kills everyone (men, women, children, infants, newborns) in Sodom and Gomorrah by raining "fire and brimstone from the Lord out of heaven." Well, almost everyone -- he spares the "just and righteous" Lot and his family.