Alexander Luthor, Jr. was born on Earth-Three - which isn't in the primary timeline that you see in standard DC continuity - and, as such, he is the son of the Lex Luthor (and the Lois Lane) from that continuity and not the Lex Luthor that every comic book reader knows so well. When the Anti-Monitor went on a multiple universe destroying rampage, by virtue of a massive anti-matter wave, in the Crisis on Infinite Earths story arc, Luthor's parents placed him in an experimental device which they hoped would carry him to the relative safety of Earth-One. It worked and he materialised on the abandoned satellite that used to be the Justice League's headquarters. The superheroine Harbinger then took him in, at the request of the Monitor. His route to Earth-One, which took him on a journey through an anti-matter storm, granted him power over both matter and anti-matter, which dramatically accelerated his ageing. As a result, by the end of that storyline, he was already a young adult and he helped the heroes against the Anti-Monitor. However, after being one of only a few to survive the ensuing multiverse-destroying events, he retreated and later returned as a villain, embittered by the failures of Earth's heroes and intent on restoring the multiverse at any cost - displaying incredible intelligence and manipulation skills in the process. He put together a plot that saw him doing things like posing and passing for Lex Luthor (humiliating him in the process and, when Lex tracked him down and asked who he was, he replied "I'm you, only better"), recruiting villains to do very specific and pre-planned things for him that would come together to complete his plans, manipulating the Spectre himself (one of the most powerful beings in all of comics) in to destroying all magic, and taking control of Brother Eye from Batman, which gave him control over the powerful OMACs and all of Checkmate's files on Earth's meta-humans. Perhaps most impressively, he managed to programme the Multiverse Tower - which was made from the abstract being the Anti-Monitor's corpse - which enabled it to evolve, think for itself and recreate the entire multiverse that had previously been destroyed. That's right, Alexander Luthor, Jr. effectively used his intellect to recreate the entire DC multiverse.
