I've been experimentally trying to resolve this in a novelized format; something of a forward to a possible Chrono Cross novel. It's nowhere near ready to post, but I can share a few ideas. The universe of Chrono is split into two main timelines: The first timeline is the timeline of the Reptites. It is the original history of the universe. That history was rewritten when a biological construct of the Reptites/Dragonians - what would become known as Lavos - went back in time to destroy the history of its own creators. This created a paradox in which the only possible outcome is a splitting of reality in which Lavos existed in one dimension while the Reptites/Dragonians existed in the other - up to the point, in theory, where the original Lavos was created and went back in time to cause the paradox. The Dragonian timeline would then - probably - cease to exist since the precipitating event of the paradox would have passed and the universe would have no more reason to remain split.
Only things didn't quite work out that way. Due to the destruction of Lavos in the timeline created by its own actions, a new species - humanity - came to approach a level of technology that the Dragonians had achieved at a later moment in their own history - eons before the creation of Lavos. (The Dragon entities are something of a precursor to what Lavos would later become.) The time-traveling outpost of Chronopolis unwittingly made contact with this dimension when it attempted a supposedly routine "counter-time experiment", and a series of tragic events were then set into motion - culminating in yet another dimensional split caused by the actions of Schala/Kid Ashtear in saving the life of Serge Krayton as a young boy.
It should be noted that this theory plays fast and loose with established canon, but I've basically thrown off those shackles to try and fix the narrative problems with the plot. I stick as close as I can to the spirit of the original material, but I know that my own plot may turn out to be no less nightmarish than what Kato and co. had come up with. Like I said, it's a work in progress.