> Just wondering...
>
> How exactly does lex view bats as an enemy of his, and how does bats view lex luthor?

Lex views Batman as being a slightly ridiculous man (he wears a costume) who is a lot more dangerous than most people realise. He appreciates that Batman has made his mark without benefit of alien powers, but if he were to get in his way, I'm pretty sure he'd be confident he could crush him.

Batman views Lex as a brilliant, utterly ruthless, murderous, megalomaniac, and ironically it's possibly only his insane obsession on Superman that keeps him from becoming the massively respected man he longs to be.

> How does the Joker view Superman as an enemy? And how does Supes view the Joker?

Joker > Superman - He doesn't, IMHO, he may carry out a crime spree in Metropolis for the heck of it (as he did shortly after Man of Steel, when he kidnapped Lois, Jimmy and Perry to pass the time), but Superman isn't on his radar, and I doubt he views him as any more "real" than he views anyone other than Batman.

Superman >Joke - views him as a dangerously unpredictable psycho. If he's bad enough to worry Batman then there must be something extra dangerous about him, and he should never be underestimated.