Fight to the death who wins no hold bars
As it stands, Iron Man and Cable take this. Neither Joker nor Luthor are able to do anything on their own to Iron Man and Cable - who are each generally more well-armed and trained in combat than Joker or Luthor - either solo or as a team. You would need to provide a lot more detail regarding the circumstances of this battle to keep it from being a humiliating rapestomp. Given sufficient prep and equipment, it could be a different story.
Also, as this is a fight to the death, I'm pretty sure Cable would be a lot more willing to finish off Joker and/or Luthor than Iron Man would be, so that's not exactly a detriment to their chances either. Although, that's probably a moot point since the OP specifies no holds barred.
Under the assumption that this is their present incarnations, and everyone is morals-off, Team 2 absolutely stomps.
Lex Luthor is a genius sure, but so is Iron Man. I don't think his powered armor is anywhere near Iron Man's though, and he probably isn't as versed in combat as Stark is. As for Joker, much as I love him, he doesn't stand a chance against Cable. Joker is a manipulator whose greatest combat feat was what - beating Luthor in Salvation Run? Cable is a soldier who has been trained for war his entire life. He's learned from the best, and even his standard loadout is always armed to the teeth. Added to the fact that Team 2 is also morals-off, I think they take this easy, especially with no prep for Team 1.