Is Homosexuality Punishable By Death?

Punishment of death is only actionable in two circumstances in the Quran.

(1) As a retribution for causing 'fasaad' (gross mischief / evil, beyond all bounds) in the land (punishable by the state)
(2) As a retribution for murder (punishable by the state).

Unlike the Bible (Leviticus 20:13), there is no punishment for death for homosexuality in the Quran. However, the Quran deems homosexuality as a sinful transgression, a 'fahisha' and it attracts condemnation and some form of retribution if one does not repent (for an Islamic state to decide based on circumstances). Verse 4:16-17 makes this clear.

004.016
"And as for the two of you who are guilty thereof, then punish them both. But if they repent and amend, then let them be. Indeed! God is Oft-Forgiving, Most Merciful."

From a Quran's perspective, homosexuality runs contrary to the nature of humans where genders of opposite sex have been created for intimate relationships and procreation through 'lawful marriage' (Nikaah) . The practice of homosexuality has also been severely rebuked in the example captured in the narratives regarding the People of Lot.

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"And Lot when he said to his people "Do you commit lewdness (Arabic: fahishata) such as no people in creation (ever) committed before you? Indeed, you approach men lustfully in preference to women. Nay, you are a people transgressing beyond bounds / committing excesses"

I hope this helps,
Joseph.