jynx I'd argue that Lelouch isn't really a villain.
The whole anti-hero archtype in general I wouldn't classify as stritcly villainous, unless they are clearly set up as a sort of antagonist, which in turn means that the same character cannot be the protagonist. I guess the only exception to this rule would be Light Yagami, since he is the only anti-hero character who is genuinely evil while at the same time being the protagonist.
Gilgamesh works, although he doesn't really have a meaningful purpose imo. The only reason why he gets in people's way is to troll the living shit out of them, which I find hilarious.