Lamech's argument continues in Targum Pseudo-Jonathan on (Genesis 4:24). He does a piece of theological arithmetic in front of his wives.
"For Cain who sinned and was converted by repentance, had protection unto seven generations extended to him: and to Lemek, the son of his son, who hath not sinned, it is just that it shall be extended unto seventy and seven."
Lamech's logic: if Cain — a murderer who repented — got seven generations of divine protection, surely Lamech, a descendant who has not murdered anyone, deserves more. Eleven times more. Seventy-seven generations.
The argument also preserves a remarkable tradition: the Targumist says Cain repented. Jewish tradition has always held that repentance is possible even for the worst of sinners. Cain, in some midrashic readings, wandered the earth in genuine remorse, and his protection was a reflection of his inner change, not a blanket pardon. Lamech is simply asking that a descendant with clean hands receive at least what the repentant ancestor received.