...all of this was explained in the last few episodes.
Zero Requiem came about largely due to Lelouch's guilt over his "mistakes" - mainly, things like Euphie's death, Shirley's death, Nunnally's supposed death, etc. None of these were his fault, but he still blamed himself. And, by that point, his life basically had no value to him. He'd lost everything. Euphie died, Shirley died, Nunnally supposedly died, the Black Knights betrayed him, and everything he'd fought for with regard to avenging his mother's death turned out to be a lie. (Ironic, considering that Charles and V.V. - and Marianne, by extension - were trying to create a world without lies.) So the least he could do was go out with a bang and at least try to make the world a better place for the few he cared about who were still alive. So that Nunnally's dream would be realized, even if she wasn't around to experience it.
Toward these purposes, Lelouch usurped the Britannian throne and took over the world. He made himself look like a tyrant in order to make the whole world hate him. Then, by removing that hate, by having Zero publicly assassinate him, the world could be united for once in peace, and Zero would be raised up to a symbol of justice. By all accounts, it should've failed, but it's Lelouch, so he pulled it off.
As for Suzaku's reasons for helping...well, to start with, he'd originally wanted to kill Lelouch in the first place after what happened to Euphie, largely because he wasn't aware of the context. For that same reason, he wanted for Lelouch to repent. And, really, he wanted his own chance to redeem himself for everything he'd done, which he got by taking on the role of Zero, defender of justice. And it didn't hurt that part of the purpose was to redeem Euphie's name...it's hard to remember to hate the massacre princess when the demon emperor is far more menacing.