It needs some work, but yeah
It's the year 2400-ish. You are a young boy (with green hair this time) living in a colony on one of the moons. You have been there your entire life. Humanity is prosperous and live hand in hand with Demi-Humans. The world is united under one banner and the whole thing is kind of reminiscent of Star Trek in terms of human society. Your father and mother are both scientists. Your mother (divorced from your father) is on earth researching an ancient civilization's technology that is considered cutting edge for 2400-ish's time. All other information is deemed classified. Your father, who you live with on the moon, is working in the labs almost all the time on something also deemed classified. One day, you receive a letter from your mother to come and visit her on earth, a place you've never been. Somewhat shocked by this (since she always came to visit you on the moon) you ask your father, but he forbids it. So you and your Unlucky Childhood Friend hatch a plan to escape the moon colony and go visit your mother, who you haven't seen in over a year. You arrive at the dig site and she seems almost too overjoyed and relieved to see you. She starts babbling things about your father and about how he understands nothing and that he is only destroying the future. But then, the dig site is attacked by a mysterious organization, an event which you actually foresaw in bits and pieces right before it happaned. Despite your best efforts to save the archeologists, your mother is killed by the Big Bad leader guy and their prized find (a device which looks suspiciously like the time machine from Chrono Trigger) is stolen. The bad guys escape and the government comes in to investigate, and learn of your unique ability.
What you do from there is entirely up to you. You have a whole world to explore (Including El Nido).
If you choose to follow the main story, you find out that the group who attacked the dig site and killed your mother is a terrorist organization who call themselves the "Agents of FATE" and that they have taken your mother's device to the moon colony where your father works. You follow them, hoping to find some answers and avenge your mother and when you arrive expecting to find the place under attack, you find out that everything is fine and that your father is far more happy to see you than you thought he would (he was very cold and abrasive before). He says that he shouldn't have let you out of his sight and that he's sorry for being a bad father. He then says that he has something important to show you. He takes you to his lab and he reveals that he's been conducting research on a dormant alien life form that they found crash landed on the moon, which is in fact another Lavos. Of course, no one knows this until you start having visions of Chrono, Marle, and Lucca during their first face-to-face encounter with it (similar to how Serge saw spectral memories of them in Chrono Cross). You hear them call it Lavos and you alarm your father by knowing its name (which also raises the question as to how your father knows its name). As he is about to explain why he brought you there, the Big Bad shows up with the Time Machine and begins talking to your father as if they are in league. The Big Bad says that its time and that they must "Put Lavos (question answered) in his rightful place in the timeline" and that "FATE demands it." Your father refuses but is swatted away by the Big Bad. Boss fight ensues and you and your compatriots escape by jumping into the Time Machine. You receive a vision that shows you how to activate it and you are all transported to the year 2800 AD.
Things are similar to how they were in Chrono Trigger during 2300 AD with a Crapsack World caused by the introduction of Lavos to the earth. You eventually learn that without knowledge of how to work the Time Machine, the Agents of FATE sent Lavos to earth in 2400-ish. You then get some more visions hinting that this Lavos must have been different to not need as long to feed off of the planet. You eventually find a way to travel through time again and your first move is to save your mother by clearing everyone out of the dig site a few days early (by basically pulling a fire alarm without revealing yourself to your mother) and to destroy the time machine. After doing so, you return home to the moon base thinking all is well only to discover that there is another you and that he never left the moon base after hearing that his mother's dig site was attacked, after which his mother came to the moon to visit him herself and that you are the result of a future that could have been. This means that the other you has no idea what's going on and never discovered his ability to see things in both future and past.
You convince your father to let you into the room holding Lavos so that you can destroy it but on arrival you find that the Ao F and the Big Bad are already there waiting for you with the other half of Lucca's time machine/teleporter thing. Big Bad explains that their goal is to send "Lavos II" back to when it was supposed to have crashed in Chrono Trigger, presumably creating a faster apocalypse due to its faster working. Your father strongly opposes and he is killed. Boss Fight ensues and you (being much stronger than before) incapacitate the Big Bad and subsequently destroy Lavos before it can be sent back. Then the other you and his mother enter and see what's happened, when the Big Bad wakes up and realizes that you are in fact a nonexistent possibility and banishes you to the newly created (from your meddling in time) Dead Sea before you can destroy the other time machine. After escaping the dead sea by using the Fiddler Crab (a la Chrono Cross) you go back to the moon to once again find the place in shambles and your mother critically wounded. She explains that the Big Bad has taken the other you in the time machine (which is now busted) and that there's something you should know. She succumbs to her wounds before she can tell you. Using visions of Lucca triggered by experiencing sights or smells that invoke memory you learn how to fix the time machine and you're off to kick Big Bad ass and literally save yourself (the real you at least).
You find yourself on the moon thousands of years in the past when Lavos was supposed to have descended from the heavens and find the Big Bad and the other you waiting. Big Bad tells you that he is quite literally an agent of the FATE system (or what life energy is left of it) from Chrono Cross (he became one by experiencing the same visions you do, only it was in much more detail) and that "Lavos II" must be sent to its rightful place. You are confused because you already killed the dormant Lavos. Big Bad tells you that you are Lavos II and in turn, the Lavos from Chrono Trigger which would later fuse with Schala to become the Time Devourer that would be written out of existence in Chrono Cross, which is revealed to be what set your present into motion. You ask how that can be possible and he says that you were a clone that the original Lavos (the one you killed) spontaneously made when it came into contact with humans (this is presumably what your mom wanted to tell you and why your father never let you leave) in human form and because you are a spontaneous clone, you will take much longer to become un-dormant. your parents raised you as their own (both of them being the leaders of the expedition) and a vision (now referred to as "memories" because this chronological cycle has happened thousands and thousands of times) confirms it. Big Bad says that the memories are FATE's way of telling you that you must go back and become Lavos from Chrono Trigger in order to set in motion the events that will create the perfect world you lived in.
Once again, what you do from there is entirely up to you. You can fulfill your destiny and essentially save the world by attempting to destroy it which allows the events of Chrono Trigger and Cross to happen and send your other self back to his time to live out the rest of his life (you dont technically exist anyway), or you can "break" the chronology by killing the Big Bad and deciding that you will not be a puppet of FATE any longer. You go back to your time, which only now exists in the Dead Sea and live out the rest of your life. You never know what happens to the real world because you never leave. Or you could send your other self back to be Lavos and live life for yourself (although doing this would merit a selfishly bad ending).
