Recently the situation involving Lex Luthor has taken a shocking twist. Lex Luthor has recently gone into hiding, preparing to try and activate mind control programming inside the brain of the current Superboy Conner Kent (created using Lex's DNA) to help him gain revenge against Earth's mightiest heroes. He also was revealed to have orchestrated, with help from the newly created robotic Brainiac, the murder of Teen Titan member Donna Troy, who is destined to play a critical role in "Infinite Crisis". He's also been carefully surveilling the new Supergirl, and has plans for her involving his newly-acquired black kryptonite.
With the real Lex Luthor acting in secret, the return of the son of the Earth-Three Lex Luthor, Alexander Luthor, Jr. has created havoc for the DC Universe. Assuming the Post-Crisis Lex Luthor's identity, Alexander has recently begun an elaborate scheme with help from the Earth-Prime Superboy. Alexander told Kal-L, the Earth-Two Superman that he wishes to restore his original universe (the world of DC Comics' Golden Age), but his intentions seem much more sinister, as he told Superboy Kal-L would help them "whether [he] likes it or not".
As one of the premier reformers of the "Secret Society of Super-Villains", Alex Luthor has recruited Black Adam, Doctor Psycho, Calculator, Talia Head, and Deathstroke as his inner circle. The new Society exploited the villain community's fear of mind-wipes at the hands of the Justice League to recruit a literal army of villains under the guise of creating their own "mind-wipe" device designed to erase the memories of Earth's heroes as payback. However, this is just another cover for his even darker scheme involving the kidnapping heroes, each representing alternate earths, to power the giant tower being used to perform a major act of alteration to reality. It is not yet clear whether Alex's goal is the restoration of the entire multiverse, the transformation of the DC Universe into a single universe resembling one of the pre-Crisis Earths (as he told the Golden Age Superman), or something else even more complex or dangerous entirely.
Not one to sit back and watch his identity be usurped, Lex Luthor took the identity of Mockingbird and formed a super-villain version of the Secret Six, whose purpose was to subvert the Society. He swore vengeance against the impostor for taking his place, though after finding Alex, he was forced to flee after it was revealed that Alex can subvert Lex's mind when they are in close proximity.
Earth-Three
In much the same way that Superman and other heroes have evil analogs on the parallel world of Earth-Three, Luthor had a heroic counterpart there. Alexander Luthor was the only superhero in that world's history, and reluctantly decided to adopt a heroic identity to combat his world's analog of the Justice League, the evil Crime Syndicate of America. This version, who eventually married the Lois Lane of Earth-Three, died in Crisis on Infinite Earths, but was survived by their son, Alexander Luthor, Jr.
In the late 1990s JLA: Earth 2 graphic novel, an updated version of Earth-Three and its version of Luthor were reintroduced to the post-Crisis DC Universe. The physical appearance of this Lex resembles the Pre-Crisis Earth-One version from 1983s Action Comics (down to the battlesuit he wears). In this version of events, the heroic Luthor travelled from his Earth (located in an anti-matter universe rather than an alternate positive one) to the mainstream DC Earth, and asked the Justice League to help him rebuild his world. However, since "evil always wins" in this alternate world, the attempt failed, and Luthor resigned himself to being the only noble character on his Earth until he formed the Justice Underground.