Hey, this is my first post. Nice to meet everybody.
I've recently regained interest in Chrono Cross and have been doing extensive research on the game (though I'm having a lot of trouble understanding certain aspects due to the language used on this site. Ex. The Dead Sea).
There is one part in particular that I would like some clarification on... Based on what I've read here, because Serge's existence in Home World means that Crono and his team never fought or discovered Lavos because they technically didn't exist to begin with, wouldn't that also mean that Lavos never existed? I mean, if everything that occurred before the year 1010 A.D is just a carbon copy of the past, wouldn't that also suggest that the story of Lavos would only exist in history texts, but couldn't happen?
I've looked on this site for an answer, but am not finding anything that explains this. Any help on this subject would be greatly appreciated. Thanks.
Hello and welcome! I was once a very active user on this site and have very recently returned - so my knowledge on some the finer details on the series has since diminished but I will give the best answer I can. Hopefully others will be able to elaborate better.
First of all, time has a funny way of working in the Chrono Trigger/Cross universe. To answer a part of your question directly, Serge's life being saved by Kid and the dimensional split because of it that followed did not render Crono and Co. or Lavos to no longer exist. To understand what happened we have to look at how time operates in the Cronoverse.
Events of the games suggest that before a single time travel event can change the course of history, the entire timeline plays out. For example:
In Chrono Trigger, though the group would eventually save 2300AD from becoming a barren wasteland due the the destruction of 1999AD, until it that act is performed by the group, they still see a ruined 2300AD when they first visit. Originally, Belthasar, when sent to the far future by Lavos, encounters the ruined 2300AD and builds the Epoch, eventually loses his mind and passes away soon after. Once Crono and Co. ACTUALLY save the future, the timeline plays out all the way through and Belthasar now ends up in the saved 2300AD where he builds Chronopolis. Then, through faulty experimentation, Chronopolis is sent back in time - the planet balances this by introducing Dinopolis and their war occurs. The timeline plays out through all the events that follow and Serge is killed. Now the timeline continues, Belthasar again appears in 2300AD, the same faulty experiment occurs but this time, after arriving in the past, Belthasar, as part of his plan, saves Serge by having Kid go back in time and rescue him.
The reason for this (as I recall) is that the Lavos from 1999AD (or beyond, depending on the era in which he was killed) that was stopped from completing its plan due to Crono and Co. defeating it was sent to the Darkness Beyond Time - and pulled Schala from the Ocean Palace incident with it. Belthasar recognized the threat and created this whole plan to stop all of space-time from being consumed by the forming Time Devourer.
So, now that we have that down, I can answer your question. In Crono Cross, Another World is the dimension where Crono and Co. appear in the future, witness Lavos destroying the world, and vow to stop him. In the final iteration of the timeline for Home World, where Serge is saved and a separate dimension begins, Crono and Co. never appear in 1999AD to stop Lavos. Remember that only the Crono and Co. from one dimension did all the work in the first game. Once another dimension was created, all time travel from that point after is negated.
You may be asking "well if that is true, how did Belthasar appear in the future in Home world?" I guess the truth would be that he never did, but Chronopolis still appeared in the past many many years before Serge's life or death scenario, so the effects of Chronopolis/Dinopolis on both timelines is kept intact.
^ Hope that helps and wasn't too wordy. There may be some errors because, like I said, my knowledge of the games, especially Cross, is much weaker these days. If you have more questions about the games and why events occur the way they do, always ask! We need more people asking big questions here =)