I think the problem here is that many take in the fact you can load the normal save file after defeating Lavos, and as such, Crono and company can fight the Dream Devourer before Lavos, which can't be, since Lavos must be defeated first. If taken that out of the picture, then it's impossible for them to fight the Dream Devourer before Lavos.
And about after defeating Lavos, I'm not sure. How would they know about the Dream Devourer anyway?