If we're talking about hand-to-hand combat, Joker wins.
They both have skills in unarmed combat, but the Joker is more skilled in this art then Lex Luthor, whose skills are "barely adequate".
Also, there's no indication that Lex Luthor has used anything he invents for weaponry, whereas the Joker carries several disguised weapons with him.
So again, if it came to that, he'd lose again.
So Joker would win regardless of the terms of the match.