The name you get for beating the game as Lucas depends. If you beat a challenge, you get the special challenge name. If you just play on normal mode (which would normally give you Lucas, who you obviously already have), it randomizes between the first six special character names.
Regarding Lethe, to my knowledge, only a handful of characters can bypass it, all by utilizing the shortcut in stomach in the room with the bone worms and tiles moving over acid.
This means, to my knowledge, only 2 of the 3 main post-game final bosses can be fought with all their buffs in place.