The various Corps started showing up a couple of seasons back.
The Parallax Corps was the first on scene (Sinestro was not affiliated with them, still working with the JLA to become a hero again)
The Orange Lanterns were next. Since we brought them into the game before Larfleeze's power was explained in the comics, we gave Mongul an orange ring before defeating him. There are orange rings, which Larfleeze keeps a tight hold of. But Hector Hammand has one now.
Atrocitus showed up, and introduced the Red Lanterns to the game. They're pretty much how they are in the comics.
Carol Farris became the Star Sapphire again, which caused a lot of tension between her and Hal over how they would take care of their son. Guy Gardner, telling the Guardians off during Sinestro's trial, was banished from the GL's. But a violet ring came to him, making him a Star Sapphire (the only guy in a Corps of scantily clad babes

)
Saint Walker and Warth were the only two Blue Lanterns. But because Darkseidiest Night was going so badly, Ganthet sent out a ton of temporary blue rings into the universe. One of which is joined with Wally West. The blue rings are still out there, but I plan on exploring that soon.
The Indigo's are as enigmatic as ever.
After becoming a Green Lantern again, Sinestro joined with his Yellow Ring and merged with Parallax. Eventually Hal defeated him, and Sinestro seemingly died. But he returned during Darkseid's invasion, now the leader of the Sinestro Corps.
After the defeat of Darkseid and the Black Lanterns, the Life entity joins with Guy, making him a White Lantern.