In Ezekiel 16:49-50 we find a list of the sins of Sodom and Gomorrah.
49Now this was the sin of your sister Sodom: She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. 50They were haughty and did detestable things before me. Therefore I did away with them as you have seen.
In chapter 16 of Ezekiel an allegory comparing Jerusalem to that of an unfaithful wife (an allegory often used for idolatry throughout scripture) is employed. This is the context. Also, it is interesting that the word "detestable" is used in verse 50. This is the Hebrew word toebah and literally means "abomination." It is the word used in Leviticus regarding homosexual sin. A male lying with a male is called toebah (an abomination) in Leviticus 18:22 and 20:13.
While there is no explicit mention of homosexuality in the list of sins of Sodom and Gomorrah in Ezekiel 15:49-50, one scholar, Robert Gagnon states "On the level of allegory, Jerusalem's 'abominations' are sexual sins; on the level of reality, Jerusalem's 'abominations' are idolatrous practices." Gagnon connects toebah from Leviticus and states "in all of the Holiness Code (the book of Leviticus is often referred as the Holiness Code) only homosexual intercourse is singled out for special mention within the list of 'an abomination'." He concludes by suggesting "In Ezekiels view, the overarching rubric for the sin of Sodom is not inhospitality or homosexual behavior but human arrogance in relation to God. The focus is theocentric."
As I wrote earlier, the attempted homosexual rape found in the account of Sodom and Gomorrah is a symptom of a greater sin, that sin being idolatry. Their idolatrous practices naturally led them away from Yaweh and towards other sins (another theme in scripture) including social injustice, inhospitality and homosexual behavior. While it isn't crystal clear that verses 49 and 50 of Ezekiel 16 reference homosexuality as part of the sins of Sodom and Gomorrah, it is curious that the word toebah is used as a description of the things done before God. Would Ezekiel's readers make a connection between the word toebah (abomination) and homosexual sin since homosexual behavior is singled out for special mention as an abomination in the Levitical prohibitions? It might be a weak argument, but it is a very good possibility that the connection would have been automatic in the minds of Ezekiel's contemporaries.
Lastly, just because homosexual sin is not explicitly named as part of the list in these verses does not mean it wasn't a part of the reason for the destruction of Sodom and Gomorrah. Obviously, Ezekiel was more concerned about the sin of idolatry than the individual sins that resulted as part of the symptom of idolatrous practices. An explicit absence of a word does not necessarily mean that the idea isn't present.