Don't forget had the rapists raped the little girls Lot offered them (his own daughters) that the city presumably would be spared...certainly so if it was homosexuality that caused God's wrath rather than rape.
(Btw, many try to whitewash Lot, some interesting while others absurd, but the most hilarious explanation I got was from a Muslim who said Lot was going to MARRY his 2 virgin daughters to the ENTIRE CITY, this being after he brought it up on a lesbian video on why we were evil, he sure didn't appreciate people talking to him in the same tones of self-righteousness when I turned the tables on him just for fun and I lost count on how many angry messages I got with rationalization for it before I caught the responses the next day).
I can have some fun with the myth of Lot's daughters putting a rufie in their father's drink to steal his seed, from talking about male physiology and how if he was truly passed out unconscious and they were still able to do it then likely Lot suffered from
Priapism, in which I understand sex is painful & unpleasant for sufferers and thus might explain a less than righteous reason for why Lot didn't take part in the city's popular activities.
Of course I think it's all BS anyway. If there's any truth to it then I imagine Lot was cast out for the sin he condemned (as so many like that project into others), murdered his wife, and raped his daughters and then said they wanted it and he was the real victim, though I prefer to believe it was just a demented fantasy some jerk came up with to control the people (much like how hardcore Christians continue to invent total fabrications to justify their position to this day).
ETA: my response was to something mentioned in the now removed rant on what a poster said about S&G.
And btw, I do see the play as needlessly provoking and counterproductive...not to say there isn't a place for that (as long as it's good), but putting it in a school is guaranteed to light some metaphoric torches (IOW, trolling).