Let's stick to the facts. Lot offered his daughters, but that only infuriated the men of Sodom. The men of Sodom didn't want Lot's daughters. They wanted the angels of God.
There was the intent to rape Lot and the angels of God. Somehow the defiling nature of a man lying with a man is ignored. The abomination is overlooked. I can't imagine a worse crime than defiling an angel of God in that way.
There seems to be this overarching concern with Lot's daughters who, by the way, were not raped, and his daughters being subject to Lot. An interesting parallel as the Son is subject to the Father.
Lot did not helplessly watch the men of Sodom rape the angels of God. Lot acted, and he was called righteous by Peter, whether you can bear it or not.