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.
- According to Luka's diary, she died of an illness. It can't have been sent by Ilias as Heaven was destroyed during the Great Disaster, 30 years before the events of Paradox. Lucifina would have died after this happened if this Luka is still between the age of 15-18. While this world's Ilias is still alive, I doubt she would have had the power to do something as petty as send an illness to kill her for revenge.
- 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 her. That said, this Lucifina could very well be alive. If she is dead, it doesn't mean we won't ever see Lucifina in the story. We'll at least see one from an alternate reality.