Salaam. Why does it say it say in the Quran (I'm reading saheeh translation)"do you desire men instead of woman" about people of Lut.Desire is not something you can control but action is? If the desire is a test then it shouldn't be acted on. Also why did Lut give his daughters? The daughters are innocent and homisexuals can't be fixed by having intercourse with woman ?
The actual phrase the Quran uses is “approach men with desire”, which is an euphemism for sexual intercourse. For more on the Quran and homosexuality please see: Did God destroy the People of Lot for rape instead of homosexuality?
As for Lot offering his daughters, please see: Is homosexuality more evil than rape in the Quran? Not exactly