Dora Bas Rivka Silver O'H
You may recall that Lot was living in Sodom. The two angels proceeded to his house. (Why two? The mission of the third angel was to announce Yitzchak's birth. He already did his job and had left.) Lot, having been raised in Avraham's house, was accustomed to being hospitable. He invited the two travelers to be his guests. They initially balked, but he eventually persuaded them.
Sodom, however, was not known for its hospitality - quite the opposite, in fact! The people surrounded Lot's house and demanded that he send out the guests so that they might "know" them (in the Biblical sense, hence "sodomy"). Lot tried to dissuade them by offering the townsfolk his unmarried daughters. (This may seem incomprehensible to us, but ancient Middle Eastern mores required protection of the guests even to this extent. Compare with the concepts of asylum, sanctuary and hiketeia.) The Sodomites refused this offer and started to storm Lot's house. They resented Lot, an outsider, setting himself an a moral authority over them. As they started to break in, the angels protected the inhabitants of Lot's house by striking the attackers blind.
The angels instructed Lot to gather all the members of his household and to get out of town, as the city was about to come down all around them. Lot told this to his daughters' fiances, who didn't believe him and refused to go. The angels grabbed Lot, his wife and their daughters and dragged them out before the destruction could start. They were instructed to literally head for the hills and not to look back. (They weren't all that righteous and they were being saved mostly as a courtesy to Avraham, so they weren't deserving to see the others being punished.) Lot was afraid that they wouldn't reach the mountains in time and he asked if perhaps a suburb might be spared as a place of refuge.