system
Given the following post, respond as if you're commenting on Reddit:
human
[DC] What if Lex Luthor hated Batman instead of Superman?

In an alternate reality, Lex Luthor never begins a one war against Superman, rationalizing that the benefits of the Kal-El's existence far outweighs Lex's concerns about him. 

Instead, Lex looks towards Gotham. He's been hearing numerous rumors about a bat shaped creature terrorizing criminals and organized crime figures there.

Since Lex secretly benefits from organized crime, having come from a rough background in Metropolis himself, this sets a bad precedent, and whatever Batman is, he must be made an example of so nobody his *his* hometown gets any funny ideas. 

This is towards the beginning of Batman's career, perhaps his second year.
gpt
Ironically, it would be *so much worse* for Lex.   
You see, Superman, for all his power, is basically a boyscout. He roughs criminals up and throw them to jail. Batman is different. He terrifies people. He gets under your skin and makes you paranoid. You know that at any given moment, he could be watching you from the shadow. And despite the fact that Superman is NOT stupid, Batman's intellect and willpower are far more scary.  
There is a reason why pretty much all of Batman's enemies are in an asylum while most of Superman's enemies are in prison. One would have to be insane to antagonize the Bat.   
Add to this that Bruce is not only a vigilante/superhero, he's also the boss of Wayne's Industries, and that he could fight Lex in business as well as in the streets, and things suddenly don't look very good for the ol' Baldie.