Spoiler warning: Below is a summary of the begining portion of Galerians: Ash, to give interested parties a sense of what this game is REALLY about, after all the misreporting that's gone on in relation to it's plot. This document is, naturally, laden with spoilers for both games, so don't read it if you don't want to know.
The game begins with a recap (full of footage from the OAV) courtesy of Lilia of the events of the first game up to the confrontation with Cain.
The game proper starts with Lilia calling Rion's name, and 14-year-old Rion sensing the call in the Family Program room in Mushroom Tower right after the fight with Cain. Rion and Lilia proceed from there into uncharted territory-- the Dome Area. Entering this new upper portion of Mushroom Tower, Rion hears Lilia's voice speaking telepathically to him, though she is standing right next to him. The intrusion of this voice seems to cause him quite a bit of pain, and the presence behind the voice seems to guide Rion using it. (And only one of the doors is unlocked anyway.)
The voice addresses Rion again through a security robot, introducing itself as Lilia from 6 years in the future. She tells Rion that he is dead, and that he currently exists as data in Dorothy's Family Program backups. She has come to take him out, because his power will be needed in the future. Rion is sceptical, and thinks the voice is some kind of deception.
The pair proceeds to Dorothy's main system, and after Rion fights Dorothy, they activate the virus program. Rion hears Lilia's voice again, telling him that no matter how many times he loops through the process of destroying Dorothy, it won't change the fact that the mother computer still exists in the future. Rion is flung back from the access terminal, and suddenly finds himself back in the Family Program room just after killing Cain.
Rion comments to Lilia on the deja vu and begins to understand what the voice had been telling him. They go through the same areas again, and when they reach the security robot again, Rion asks the voice what he should do. (And she tells him how to get out, though I can't understand what she says.) This time, they encounter Spider, whom Lilia's voice identifies as one of the Last Galerians come to prevent him from getting to the outside world. Spider blames Rion for causing him to be created, and attacks. (This is one of the most fun boss fights ever.) After Spider is defeated, he vanishes.
Back up to Dorothy's room for another round, and as the pair activate the virus again, Lilia says to Rion, "I guess this is goodbye." Rion responds, "I'll see you again on the other side."
Rion vanishes, and Lilia is left alone with the destruction.
