Lex Luthor is based, not the least bit subtly, on Vince McMahon Jr., the owner of World Wrestling Entertainment.
Vince McMahon is a larger-than-life person (character?)--utterly titanic, charismatic, ruthless, indeed a megalomaniac. He is, in fact, likely more villainous than the AU version of Luthor.
Things both McMahon and Luthor are going to be accused of: criminal negligence.
Things McMahon has been accused of that Luthor is NOT going to be accused of: sexual harassment, sexual assault, encouraging steroid and painkiller abuse that shortened the lives of his workers, allowing writers to prey sexually on young employees (in all cases he was either found not guilty or settled out of court). Mind you, McMahon would shrug and say such allegations are the price of power and fame.
He's also famous for pretty much single-handedly destroying the old "territory" system of wrestling, creating a near-monolithic entity in the WWE. He inherited the northeastern territory from his father, but through a combination of canny marketing and borderline-unethical business dealings, slowly drove nearly everyone else out of business.
While he runs the company, he also "plays a character" of the Chairman of the Board, Vince McMahon--an over-the-top megalomaniac villain who abuses and torments his employees. Here's his amazing entrance theme:
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In fact, for a time he had a "Kiss My Ass Club," in which he would drop trou in the ring and force wrestlers to kiss his bare ass if they wanted to keep their jobs. Video below (not recommended for anyone who finds public humiliation squicky):
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(I kept the basic idea, but simply could not imagine any version of Lex Luthor making people kiss his ass, so it became feet…)
Obviously a lot of the frisson of the character is that he blurs the line between reality and kayfabe. Part of what's amazing about McMahon is his willingness to come out and "take a bump"--get thrown around for the sake of the narrative. Here he is getting tossed around by his greatest nemesis, "Stone Cold" Steve Austin (warning for blood):
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He's also famous for having a very clear physical "type" that he prefers--very big, very muscular guys--and his belief that anyone less than his ideal won't be accepted by the audience as a championship-holder (another trait I've given Luthor). Though lately even this has become part of the kayfabe, as recently they've been pushing two smaller wrestlers (C.M. Punk and Daniel Bryan) who don't "fit the mold" at all. Of course, their storyline is that evil McMahon (and his evil daughter and son-in-law, but the McMahon extended family is a whole separate post) is constantly attempting to destroy them, which obviously he's NOT, exactly, since he's promoting them and--this is where my head starts to hurt.
I've made him sound really terrible here and--well, I guess he is, actually. And yet he's so outsized and grandiose and larger than life that there's a certain amount of awe there as well. There was simply no one else in the DCU that could possibly "play" him in the AU than Lex Luthor--no one else so driven and ruthless and yet pragmatic, no one who so clearly sees themselves as the pinnacle of human evolution.