Except that's not really what happens, timelines are only erased because of the Time Devourer, and multiple timelines are shown to be able to coexist without issues. The CT cast time traveling isn't really at fault, though the moral consequences of merging all timelines and the countless lives that would be lost from that at the end of CC never gets questioned unfortunately.
I believe it's the other way around. Lavos was defeated by Crono and friends, so the timeline seen in 2300 AD was shunted to the Darkness Beyond Time and Lavos with it, whereupon it merged with Schala and began to threaten all of reality.
I don't think it's explained in-game how timelines actually split (like the timeline where Lavos never arrived and the Reptites became the dominant species), but I'm sure someone can correct me on that.