According to Islamic tradition, Lot lived in Ur and was a nephew of Ibrahim. He was commanded by God to go to the land of Sodom and Gomorra where the people were well-known for their sinful lifestyle. When he arrived there, the people ridiculed his teachings and ignored him.
While he was in Sodom and Gomorra, two angels visited Ibrahim and informed him of the impending doom faced by those cities. Ibrahim asked the angels to protect Lut and his family. They complied, and went to Lut in the guise of two handsome men. The people of Sodom and Gomorra grabbed them; Lut tried to stop the people, but was unable to. However, the angels got their message across to Lut and ordered him to leave the area and not look back.
He subsequently left with his family, once they crossed a hill, the cities were engulfed with fire. Lut's wife turned back out of her sympathy with the people, and was punished for disobeying God by being turned into a pillar of rock.
It should be noted that the Biblical stories of Lot's incestual relationship with his daughters are not considered true in Islam, as such an action would remove a man from being a prophet of God in the Islamic view.