While she does not appear in part 1, we do learn some small information about her in Luka's diary. She's still Luka's mother, and she still died of an illness. Presumably.
Lucifina is brought back to life on the Ilias Route, but due to a lack of energy, she returns as Lucifina-chan.
- According to Luka's diary, she died of an illness (While this world's Ilias is still alive and she traps herself inside the Ilias Temple as Heaven was destroyed during the Great Disaster, 30 years before the events of Paradox so she couldn't be interfered with Lucifina's lifespan and natural disease as well as has no reason to do so.). Lucifina would have died after this major event if this Luka is still between the age of 15-18.
- Lucifina didn't choose to fall in this reality. More, she was forced to due to the amount of dark energy she took in. So she didn't necessarily betray Ilias in Paradox.