Lex Luthor (Alexander Joseph Luthor) is a fictional supervillian created by DC comics as Superman's archenemy. He is a power-hungry mad scientist and the owner of LexCorp-- a vast conglomerate corporation that controls much of Superman's earth.
There are several origins that explain his beginnings, from knowing Superman as a child, to growing up in some slums and murdering his parents for insurance money. But no matter the canon being followed, Lex Luthor is very, very evil. He has done everything from holding the world hostage with a death ray to becoming President of the United States of America. Name an evil scheme, and he's done it.
Interestingly, Lex Luthor has no superpowers to speak of. Once or twice he has donned a power armor suit, but never has he permanently given himself super powers. The fact that he is such a threat to the near-omnipotent Superman without having extra-human powers himself hints to his great intellect and formidable killer instincts. He is not to be messed with, and under no circumstances is he allowed to run amok in HQ.
Lex Luthor is evil, and portraying him as otherwise accounts as OOC unless it's from a comicverse where he's not completely awful. He has several different canonical wives and love interests. His fanbase is unknown, but may be presumed to be very splintered just as his canon is from comic series to comic series. Fangirls likely will take an interest in his most recent appearances, while fanboys will agonize over the tiniest details of his canon appearances... often to stupid ends.