Why did Lot offer his two daughters in Genesis 19:8?
Answer From The Annual Reading Schedule - Week 4 Notes For Genesis: I have heard one perspective to answer this question from Jeff Benner of the Ancient Hebrew Research Center. Jeff explained it this way (paraphrasing): Notice how Lot said the men has come under the shadow of his roof in his reply in Genesis 19:8. Hospitality was so important back then, that when someone would come under your roof it was important to protect them so much that people would go out of their way to do so, in this example including to the extent of even giving away his daughters who had not yet known a man to the crazy mob outside the door.
I think that Jeff's view on this may be correct, and I also consider it a possibility that Lot realized these are messengers of Yahweh and therefore did the only things he knew to do to protect them at the time, possibly not realizing these messengers would blind the whole lot of them and protect his household all on their own.
Lot was definitely in a tough situation, having such a disgusting mob outside his home. This is similar to the disgusting situation in Judges 19:22-28 which shows, again, women being offered in place of the men, and one actually given who ends up dying. We see in Judges 20:5 the man says they were going to kill him, so perhaps it was also this kind of violence in addition to the sexual assault that was trying to be avoided when he offered his two daughters. I am not certain, however.