The Bible says only Lot was righteous, not his wife nor his daughters, who then concocted a scheme later on to rape him... Which might tell you a thing or two about them, etc...
I doubt any of them were as "tormented" by that culture in that city as Lot was being there... They were more than likely just like the rest of them there... corrupted or already compromised by that culture, etc...
But the men he (Lot) was protecting were Holy and righteous Angels of God... Should he have let them be raped...?
I wonder if the only reason Lot even stayed there was because of his wife and daughters, etc...
Either way, God for some reason considered Lot righteous, and maybe the only sole righteous one left there, and it wasn't just on account of Abraham either...
And I for one believe God, how bout you...?
God Bless!