Lex Luthor Vs. Doctor Doom- Who Would Win?

In the annals of DC and Marvel, two villains stand apart from the rest- Lex Luthor and Doctor Doom. Which of them is the superior of the two?
There are some striking similarities between these two villains- both men are obsessed with destroying their nemesis to the detriment of nearly everything else in their lives. Both men are among the smartest on their respective planets. Both really like the color green, although Doom's shade is darker than the one Lex prefers.

If these two villains were to clash, which one would be the victor? Would Lex take out Doom? Or would Doom teach Lex a painful lesson in who's the best?

No prep

Location Blue Area of the Moon

Round 1. Hand to hand fight, without armor, powers, or weapons.
Round 2. Hand to hand fight, with armor.
Round 3. All weapons and armor related abilities allowed.
Round 4. Lex Luthor Vs Doctor Doom in Chess

Who wins and how?