In a fist fight, Luthor is mush. But Luthor doesn't fight with his fists.
Given 3 months, Luthor would have all the information he needs to keep himself alive. Blackmail is like Luthor's favorite hobby.
Anyone Thor's ever cared for would be under hired watch. Better believe Bullseye, Deadpool(considered a hero sometimes, but remember, he's a mercenary, so he is fair game), and a whole shitload of others that Lex can hire would be keeping tabs on the humans and lesser heros that Thor cares for, while having a small remote handy to set off the nuclear bombs he had his hired supervillans plant all around the Avengers hideout. He'd have bankrupted Stark Industries, bought the company, and taken all the information on the Ironman tech. to have his top scientists build him an army of men in Ironman armor, and probably give new models to his hired supervillans.
Thor would never lay a finger on him.
Lex can't fight hand to hand worth a shit, but he's never out of options. He's got more money/power/influence than God, and knows how to use it.