The Ten Commandments do not cover every specific sin or prohibition in the Bible, including gay lifestyles, but broadly summarize the Old Testament commandments. However, that does not mean that gay lifestyles and practices are acceptable to God because of their absence in the Ten Commandments.
The Bible, in its entirety, is God-breathed, meaning that God inspired every word recorded by its authors throughout the Old and New Testaments. 2 Timothy 3:16 says, “All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; so that the man of God may be adequate, equipped for every good work.” It also states in 2 Peter 1:20-21, “But know this first of all, that no prophecy of Scripture is a matter of one’s own interpretation, for no prophecy was ever made by an act of human will, but men moved by the Holy Spirit spoke from God.”
Therefore, every command, directive, prohibition, instruction, doctrine, truth, declaration, warning, and fact contained in the Old and New Testaments is equally as inspired as those in the Ten Commandments because they are all God’s Word. Psalm 119:160 says, “The entirety of Your word is truth, and every one of Your righteous judgments endures forever.” Likewise, Psalm 19:7-8 says, “The law of the Lord is perfect, restoring the soul; the testimony of the Lord is sure, making wise the simple. The precepts of the Lord are right, rejoicing the heart; the commandment of the Lord is pure, enlightening the eyes.”
Consequently, although gay lifestyles, relationships, and activities are not specifically addressed in the Ten Commandments, they are identified as sinful elsewhere in Scripture and, therefore, should be rejected as viable options—not practiced or supported (see Leviticus 18:22-30, 20:13, 1 Corinthians 6:9-10, and Romans 1:26-32).
I hope the above information has clarified why gay lifestyles are not specifically mentioned in the Ten Commandments, yet are still prohibited by God.