"If Lex Luthor Were Superman's Father" DOES happen in continuity, but because Luthor only DREAMS of succeeding, the Superman he's trying to create by changing history remains imaginary. But let's not get ahead of ourselves. This Silver Age classic starts with Luthor escaping from prison by faking a heart attack and tricking a doctor into making a formula that temporarily turns him into a giant. I did say Silver Age. In his lair, Lex uses a timescope to watch baby Kal-El getting shot to Earth from Krypton and he gets a brilliant idea. He goes back in time with his timeship, to the days before Jor-El and Lara were engaged, and posing as "Luthor the Noble", a cosmic cop from another world (and wearing an anti-grav belt to sustain Krypton's high Gs), tells everyone Kandor is about to be taken by Brainiac. No one believes him except Lara, who kind of swoons when he's proven right.
So Luthor pours on the charm and he and Lara become inseparable, touring the crazy SF sights of Krypton while jealously looks on. When he's out of town on an exploratory mission, Luthor uses his alone time with Lara to pop the question:
She says yes! And that's when the imaginary bits of the story kick in. Luthor sees it all unfold in his mind:
Ok, if I can punch holes into his plan here... First, why would the baby he has with Lara be called Kal-El? Would you let your wife give your son her ex's last name? No, that's ridiculous. And would that baby become Superman? His half-human DNA would certain depower him, for one thing, and instead of keeping history on track by sending him off on a rocket, why not bring him back to 1964 Earth with you and raise him as your own super-powered minion? Why even HAVE a baby with Lara? Wouldn't keeping her and Jor-El apart be enough to erase Superman from history entirely? Couldn't Luthor return to Earth before Krypton explodes to find a world with no Superman, and where a good Luthor with hair is puttering away somewhere? Couldn't evil Luthor then do whatever the heck he wanted? He wouldn't even have a criminal record! But that's all moot because just as he's about to put a wedding ring on Lara's finger, his anti-grav belt's batteries give out!
That's an especially lame deus ex machina, given that Jor-El was racing to get to the chapel on time to stop the wedding. He doesn't make it. There just happens to be a miracle. So Luthor is rumbled and his web of lies comes apart. He runs, flies back to the present while watching through his shipboard timescope how his relationship with Lara only made her realize it's Jor-El she really loved. Ah. Well, good thing she didn't go through with it, then. He materializes right in Superman's path and is sent back to jail. And the Man of Steel never found out how close his greatest enemy came to banging his mom.