I’ve heard conjecture made that Lot was trying to placate the citizens of Sodom merely, and wouldn’t have given them his daughters if accepted (he knew they wouldn’t accept.) I’ve also heard that he was testing them, thereby making their judgement all the more severe.
Weak, but that’s out there.
I don’t have a teen daughter, just a son. But there is NO power on this earth that would EVER make me say something like that... testing or not.