We start with the League confronting Lex Luthor in the White House, where he threatens to destroy the world, boasting that no matter what Superman does Lex will always return and Superman needs him as a villain to receive the adulation of a hero. Realizing the truth, Superman kills Lex. Two years later...we realize we're in an alternate dimension as the Justice Lords (absent a deceased Flash) now keep the world under its "benevolent" thumb to eliminate crime and suppress all dissent. Their Batman learns of "our" Earth and its Justice League, and that they haven't dealt with Lex Luthor. The alternate J'onn travels there and lures the League back to their world, where they are caught and imprisoned, Hawkgirl being badly injured in the process.
The Lords, pretending to be the League, must rise to their first challenge - an alien conqueror named Doomsday arrives on Earth and even the Lords seem helpless before him . . . until the alternate Superman uses his heat vision to lobotomize the would-be conqueror. And the inhabitants of Earth are left to wonder if this new policy is what they want, or if it goes too far.
Doomsday first appeared in Superman: The Man of Steel #17 and was presumably created for the purposes of killing Superman in the comics. Created by Kryptonian scientists before the destruction of their planet, he eventually made his way to Earth and "killed" Superman. He has been seemingly destroyed again and again, but has the ability to evolve to meet and defeat any threat. Oddly, he doesn't appear in "Hereafter (1)", which has Superman dying. This is his first appearance in the WB animated universe.
The Justice Lords
While there is no group named the "Justice Lords" in the comics, the Justice Lords here bear some small resemblence to the Crime Syndicate of Amerika, formerly the Crime Syndicate of Earth-3. Given this is the "third" Earth we see in the animated series, this dimension might be "Earth-3" too. However, the Justice Lords bear a stronger resemblence in concept to a fascist Justice League that appeared in Justice League America #72-75, that featured a darker version of the existing Justice League in its late 70s/early 80s "Satellite era" incarnation taking over the Earth and imposing a fascist state to fight crime. Ironically, this League turned out to be a creation of Dr. Destiny. There are also some similarities to the Squadron Supreme at Marvel (who were based off of the JLA) and The Authority.