PLEASE, NO SPOILERS
I started watching Gurren Lagann knowing nothing (I only knew that Kamina dies) and I just finished watching episode 15. They just defeated the Spiral King???? But there are still 12 episodes left, what the hell is going to happen after that? Defeating Lordgenome was the main objective and it was accomplished, so what else is there?
My theory is that it's aliens. "When a million monkeys have stepped on the surface, the Moon will be the messenger of Hell and destroy the world of the Spiral." If I'm not mistaken, episode 1 begins with a scene in space, so I think that phrase from King Lordgenome refers to aliens. Leaving the humans on the surface was a way for some alien race not to see the humans. But now that they are going to occupy the surface, the aliens will notice and come to attack.
Anyway, I think that's it. Again, I ask that you don't give any spoilers in the comments. Watching without knowing anything has been a great experience.