Okay, here's some ideas:
First movie starts off with either Green Lantern or Superman (one of the intergalactic capable heroes) investigating a dead planet that is in ruins, where the populace basically exterminated itself in a horrific war, and the audience catches a few glimpses of the Omega symbol as a little bit of foreshadowing for future films. The hero then discovers that something slipped away from the planet and has arrived on Earth. We are then introduced to this film's bad guy, Despero. Armed with regenerative abilities and supreme telepathic powers alongside some superhuman strength, Despero begins inciting Humanity to turn on itself, which our heroes think means that he's the one who wiped out the previous planet. His main manner of attacking others is to control someone (Superman most likely, so we can see how all the other heroes could concievably take him down) to fight the others, and his endgame gambit of launching a World War in which he will dominate the minds of the winner is defeated by the League. The League's formation reveals two things: they truly are respected and feared as the new superpower on the planet, despite their protests and lack of any evil ambitions, and Despero reveals he was trying to conquer the planet, and mentions that the dead planet was somebody else's handiework. Someone much worse...
Second film features a nasty reaction against the world by those who fear them. Lex Luthor participates in the founding of a Legion of villains to oppose them, including individuals like Vandal Savage and Ra's Al Ghul as members of the inner council and Luthor inviting the Joker around as a kingmaker among his other allies/rivals, with probably some kind of advertising and arc word like "Are you League, or are you Legion?" Luthor spends a portion of the film running for President, at least partly as a way of screwing with Superman and exposing the number of people who fear and hate out heroes. We becom aware that some of these anti-heroics humans are having strange patterns of behaviour and stuff like the Crime Bible is happening. The Legion attains some, but not all of Batman's plans against the League, and seem to successfully capture or incapacitate every hero except the Flash, who was warned by Batman before hand with the help of Superman. Flash frees the heroes and they defeat the villains, publicly humiliating Luthor and ending his candidacy, though the Legion goes underground, beaten but not broken.
Third movie introduces a gradually worsening world in which the League is slowly falling out of favor, with the Legion believing they can now strike while the iron is hot with the aid of their new ally, Libra, but he misleads them and manages to bring about the possession of one of them (possibly Vandal Savage) by Darkseid, who is the dark god who orchestrated the dead planet way back in the first film. He brings along his anti-life equation and his armies of Apokilips, and the league finds itself battling about half of the world's population and cosmic horrors. The money shot for this movie will involve seeing members of the Legion, especially Luthor, fighting side by side with their greatest enemies against Darkseid's forces.
Now, since I don't feel like just ending this story at just a trilogy, here's how I have it going down: (1)Darkseid is killed by Batman, who is banished to something terrible by Darkseid's parting Omega beams.(2) Darkseid's other backup plans goes into affect, with a superweapon being stopped by the sacrifice of the Flash, who joins with the speedforce to stop him. (3) Green Lantern is corrupted by the Parallax parasite and flees the planet before loosing his mind, taking out Darkseid's remaining stellar forces at the same time. (4) Wonder Woman, in order to hold off humanity's hordes without killing them, pledges her allegiance to Ares for more power. (5) Aquaman is dethroned in Atlantis, because of his refusal to shut the place off to surface world refugees. (6) Superman faces off with the last Apokiliptikan superweapon-Doomsday, and the movie ends with it looking like the two may have just mutually killed each other.
Cue six movies that all act as sequels to these individual storythreads, allowing new actors to be cast in a kind of restart that avoids a flat out reboot.
