A well worn trope in superhero comics and popular fiction in general is the hero's nemesis who doesn't want anyone else to kill the hero, as they see it as their and only their privilege to do so. Joker is often portrayed like this, having gone out of his way to save Batman from forces other than him on several occasions, and the same can be said for Doctor Doom's relationship to Reed Richards and Venom's to Spider-Man.
However, does Lex Luthor fit this trope? I know he's often portrayed as a raging egomaniac at heart, which would surely forbid him accepting anyone else claiming victory over Superman, but he has also been shown as more of a pragmatist who truly believes that Superman represents a philosophical threat to humanity. A Luthor with that mindset wouldn't care if someone else took out Superman, right? Would Luthors from different publishing eras have different ideas on the matter? This is a job for the resident Superman historians!