Lex Luthor is the CO of LexCorp.
The US government recruited Lex to investigate and bring down Superman. Luthor was hired by General Sam Lane to capture Superman by setting a train accident as a trap for him. The younger, weaker, inexperienced Superman barely stopped the train and was left unconscious. Lex collected Superman and subjected him to a series of tests to ascertain his strengths and weaknesses. He tortured Superman before managed to escape.
Lex Luthor was the secret caller named "Icarus" that was giving secret information on Glen Glenmorgan to Clark Kent.
Lex was in contact with the "Collector of Worlds" and made a deal with him. He was present when the Collector abducted New Troy as one of the residents in the area. He along with Lois Lane and Jimmy Olsen went into Glen Glenmorgan's hotel where Lex called the Collector. After his connection with the Collector was exposed, Luthor was fired as a consultant to the U.S. military by General Lane himself. Luthor explained that they had no evidence, and that they needed his expertise as their consultant. Lane refused to listen and had Luthor thrown off the base, but Luthor was confident that he would be asked back.
Lex Luthor played a major role in the K-Man's creation. He had stolen Kryptonite crystals from the government while being employed by them.
Luthor arranged an illegal smuggling of war machines in Qurac. Knowing that Superman would intervene, Luthor laced the weapons with Kryptonite and nanite technology in order to acquire a sample of Superman's DNA in order to create a monster based on the genetic structure of Superman known as the Hybrid. As Superman seemingly defeated the monster with his ice breath, it was later found out that the Hybrid was attacking Metropolis - whilst also having infected civilians with a virus (that was carried by Superman when he in turn was infected by poison from his earlier tussle with the war machines), as Luthor had intended. The plan by Luthor was to show the people of Metropolis that Superman was indeed an alien menace, and only Luthor could save them from the Man of Steel. The final confrontation between Kal-El and Luthor, resulted in the defeat of Lex. Luthor was arrested for the Hybrid crisis he orchestrated and placed in a a one-man prison designed specifically for him created by the U.S. government and was visited by Superman.