(The Quran condemns homosexuality in 7:80-81 but no punishment is ever specified. Presumably the punishment for homosexuality is to be left to God.)
The tale of Lot R.A. Or how Sodom and Gomorrah got obliterated is used by both Christians as well as Muslims in trying to discourage public/governmental encouragement of homosexuality, Islamic law doesn’t dictate rules about homosexuality in the personal/private sphere but taking cue from how God punished the people of Lot R.A., it does seriously condemn and discourage the same at a governmental/public level.