As the leader of the Justice League, Superman united his fellow heroes for the noble purpose of saving the world from destruction.
That's not really of interest to Lex Luthor though. All he knows is that if Superman has a nice thing, he wants to take it away.
To that end, Lex Luthor has been the founder of numerous opposite teams to the Justice League, uniting his fellow villains for the less noble purpose of beating up Superman and his friends.
The team started life as the Legion of Doom in the Super Friends cartoon before making the jump to comics. In their first appearance in JLA, Lex named the group the Injustice Gang and recruited villains for each hero on the League, including Joker (Batman), Circe (Wonder Woman) and Mirror Master (Flash).
The gang tried to turn the League against each other so that they would disband, allowing Luthor to set up a new team under his control. The plan failed when Mirror Master betrayed the group after being offered a larger paycheck by the heroes.
Lex and Joker would reform the group later though as the Injustice League, a gigantic gathering of some of DC's biggest villains. Together they were able to take down the Justice League and took them to their headquarters the Hall of Doom (sadly, unlike in the show, it was not located in the awesomely named Slaughter Swamp).
The heroes were eventually able to break free though and capture the villains, an eventuality Luthor had already planned for.
I was just a mild-mannered NCTJ accredited journalist until one day I found out the truth... that I could share my nerdy ramblings with people on the internet! It's just like mumbling to myself on the train, but without all the strange looks.