First of all, nowhere in the Bible does it tell us that Lot knew these men were Angels sent to destroy the city. He thought they were going to stay the night and depart in the morning.
Genesis 19:
1The two angels arrived at Sodom in the evening, and Lot was sitting in the gateway of the city. When he saw them, he got up to meet them and bowed down with his face to the ground.
2“My lords,” he said, “please turn aside to your servant’s house. You can wash your feet and spend the night and then go on your way early in the morning.”
“No,” they answered, “we will spend the night in the square.”
Now, by using a little common sense, we can deduce that Abraham sent word to Lot that some men were coming to see him, and that they were to be treated as Abraham's honored guests. This would make these men, more important than anyone else, in Lot's eyes, more important than his own daughters, or himself.
Genesis 19:
3But he insisted so strongly that they did go with him and entered his house. He prepared a meal for them, baking bread without yeast, and they ate.
4Before they had gone to bed, all the men from every part of the city of Sodom—both young and old—surrounded the house.
5They called to Lot, “Where are the men who came to you tonight? Bring them out to us so that we can have sex with them.”
6Lot went outside to meet them and shut the door behind him
7and said, “No, my friends. Don’t do this wicked thing.
8Look, 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.”
let me, I pray you, bring them out unto you, and do ye to them as is good in your eyes; this was a very great evil in Lot to make such an offer of his daughters; it was contrary to parental love and affection, an exposing the chastity of his daughters, which should have been his care to preserve; nor had he a power to dispose of them in such a manner: and though fornication is a lesser evil than sodomy, yet all evil is to be avoided, and even it is not to be done that good may come: nothing can be said to excuse this good man, but the hurry of spirit, and confusion of mind that he was in, not knowing what to say or do to prevent the base designs of those men; that he might be pretty certain they would not accept of his offer, their lust burning more after men than women; that this showed his great regard to the laws of hospitality, that he had rather sacrifice his daughters to their brutal lusts, than give up the men that were in his house to them; and that he might hope that this would soften their minds, and put them off of any further attempt; but after all it must be condemned as a dangerous and imprudent action:
only unto these men do nothing; for as yet he knew them not to be angels; had he, it would not have given him the concern it did, since he must have known that they were able to defend themselves, and that the sin these men offered to commit could not be perpetrated on them: but he took them for mere men, and his request is, that no injury might be done to their persons in any respect, and especially in that way which their wicked hearts put them upon, and is so shocking to nature:
for therefore came they under the shadow of my roof; for though it was not their intention in coming, nor the design of Providence in bringing them into Lot's house, to secure them from the violence of the men of Sodom, but for the preservation of Lot and his family, which as yet he knew nothing of, yet it was what Lot had in view in giving the invitation to them: and the laws of hospitality being reckoned sacred and inviolable, a man's house was accounted an asylum for strangers when taken into it.