So one time Chris Haley drew a Lex Luthor. And it looked a tiny bit like Professor Xavier to me. And then the entire universe clicked into place for me.
See, at the end of All-Star Superman Lex has given himself powers, Superman’s really, and he has a moment:

Anyway – at the end of the story Superman has gone into the sun and we’re left with this sense that maybe Lex could be a better person now.
Except he’s Lex. Look, no one will believe him and he knows it. But he might, just to see, to experiment and try to expand himself and us, explore outward. And in doing so cross universes. In his new universe Luthor has two things happen:
1) The crossing expands his mind again – he becomes a telepath.
2) The landing cripples him, physically.
But Lex looks around the Earth he has landed on and sees mutants. He sees these people with powers being shut out and not allowed to help and decides that he will learn from Superman, at long last, and truly help. He will gather them under an umbrella of peace, hope, and learning. After all he’s a genius – who better to run a school.
Of course, he’s still Lex underneath it all. So sometimes he can be a dick. Selfish and petty, motivations a bit askew, all those things that his new self, this Professor Xavier, become known for. A great man perhaps, but a bit wonky. He can even seem, at times, evil-feeling. But he tries.
So there you go. Lex Luthor is Prof. X.