The Bible doesn't judge people for their actions. The Bible reports the events. So there is no way to fully understand why Lot would offer his daughters to a group of sex-crazed men. Because we seem to only get the bare facts of the story, there are a number of reasons Lot could have done this.
First of all, it was custom during that time to protect guests at any cost. By offering his daughters in their place, maybe Lot had an escape plan. Maybe he hoped his daughter's fiancees would come to their rescue. Maybe he thought the men wouldn't be interested in the women because they were homosexuals. However none of these excuses sit well with me as a daughter and as a woman.
Lot and his family were living in a town that was overpowered by sin which is why God sent two angels to destroy the city. Soddom was so despicable it wasn't worth saving. Lot had allowed himself to succumb to the pressures of his culture instead of abiding by the laws of the Lord. So then the question is raised, "How am I allowing the pressures of the world around me depict the decisions I make on a daily basis?" I saw "how" because I am doing it. Many of us are.
Now for the question of incest. Part of me thinks, *Why does this story need to be here? I don't really want to read about two sisters having sex with their father.* But there is a reason. And incest is an issue in today's culture so of course it needed to addressed.
This part of the story is yet another example of how we can let sin in and it changes who we are and what we do. It's sad, but Lot passed on his lack of moral control to his daughters. The daughter's wanted to preserve their father's blood line and they thought sleeping with him was their only option. They weren't driven by lust, they were driven be desperation. Lot should have found his daughter's husbands a long time before this and heck, Abraham's family wasn't that far away.
Once again, this story gives us the facts so understanding why the sisters did this is hard. It also appears as if they went unpunished for their sin. However the two sons that are born are Moab, father of the Moabites of today and Ben-Ammi, father of the Ammonites of today. The Moabites and Ammonites are Israel's greatest enemies. Perhaps this is how God dealt with the sins of the sisters.
There is a cliche, the sins of our fathers are passed down for generations. This is true with abuse, racism etc. It's also true here in the context of this story.
-Abraham found favor in God's eyes and pleaded for Lot's life to be spared when God sent two angels to destroy the city.
-Lot was a weak man who cared more about his power and wealth than following God, yet God spared his life and his daughter's lives.
-Lot's daughters, following in their father's footsteps, acted out in desperation and fear and bore two sons that became the fathers of two enemies of Israel.
-Due to a family connection, Moses was forbidden to attack either of these nations.
-Ruth was a great grandmother of David and an ancestor of Jesus; yet she was a Moabite.
Of course you are free to draw your own conclusions. But I see a pattern which shows God's mercy to us as sinners and how He can make anything into something that will glorify His Kingdom.