Luthor is a decent fighter and has access to more and better technology.
Joker is completely unpredictable and actually puts up fights with Batman now and again.
I'd say it depends on what prep you give them. If you mean just a fist fight, I'd have to go with Luthor. If you mean "they see each other on the side of the street, with whatever they have in their pockets and such", I'd go with Joker, chances are he has a bomb with him or something insane like that.
Overall with prep, I'd give it to Luthor, but Joker is way cooler.
If this was a war as in using each others resources i think Joker would win brain to brain since LAST LAUGH i think that Joker has never put his full mental potential into his past plans untill he thought he was gonna die after that he basically took over half the world and defeated many super heros even infecting circe making her turn superman into a monster has he not also almost defeated superman and been able to use the philsophy stone or rock of ages which lex could not figure out Joker is probably smarter then lex but his insanity makes him just that unstable that if he wasnt totally going after luthor with all he had he would lose but if he put all his effort into it like he did in Last Laugh i think Luthor would be toast.