I don’t know much about Lex Luthor, but I do think that what I DO know of him (about him building his career from nothing, being innately talented n wtv) I think he and Bruce would have been friends.
Luthor was talented, but he was poor (iirc) this gave him the drive he needed to become successful, to prove people wrong about his status and his character.
Bruce grew up in Gotham, wealthy of course and not having the traditional struggles of a poor person, but it’s fucking GOTHAM, that comes with its own problems. Bruce’s parents were murdered in front of him, exposing him personally to the crime in Gotham and also motivating him to make the city better (not to say he wouldn’t want to better Gotham if his parents lived)
I believe that these two different but equal goals would make them friends or begrudgingly respectful.
Luthor would respect the genuine care that Wayne has for his city and his desire to make it better, and Bruce would admire Alex’s dedication and intelligence.