In Genesis we see these men as being probably bisexual, which is an abomination to God, Lev 18:22, wanting to have sexual intercourse with these two men not knowing they were angels as those from Sodom and Gomorrah lived immoral sinful lives as they lived as they pleased. Scripture does not say why Lot offered his two daughters, but it could have been to save the dignity of his two quest as they were considered more important. Tradition says visitors were placed above even the family as their well being came first. Living in Sodom made Lot complacent with his surroundings and compromised his faith and testimony of God.
In Judges 19 the Benjaminite city of Gibeah was considered another Sodom in it's depravity. There was no king to rule over them in that time and the tribe of Dan and Ephraim fell to idol worship and allowed God to be removed from them, Judges 18:30; 1 Kings12:25-33; Hosea 5:9, 11;Psalms 78:9-17, 65-67.
We read that a Levite from Ephraim who traveled to Bethlehem to bring his adulterous concubine back home and on their way back they stopped off at Gibeah. She was actually the wife of this Levite man, but a concubine to many others she prostituted herself to other men. No one would take them in except an elderly Ephraimite who lived in Gibeah. The same thing happens to them like it did with Lot that the men in that town wanted this Levite man and have sex with him. This elderly man, like Lot, told them do not so wickedly with the Levite and offered up both his daughter and the wife of the Levite, but they only took the wife/concubine and let the daughter alone. To make things even worse the Levite cut up his wife in twelve pieces and distributed them throughout Israel causing a war that almost wiped out the Benjamites