That kind of depends on your idea of "story-wise"...I mean, sure, from a game-creator's POV they aren't supposed to win there (i mean, you don't get a real ending doing that!)...But if you see it as Crono & Co. are up against Lavos now, that who they're trying to destroy, I think they are supposed to defeat it there, but Lavos's simply too powerful for 'em (either at the time for them or because Lavos's actually more powerful for some reason [which he is]).
edit: I kept referring to Lavos as "He" and I h8 that...