This Lucifina is a copy from the Lucifina in the Great Monster Wars. But they aren't the same. She is on par with Micaela, if not more powerful in single combat.
Like the other LoC bosses, you can't talk to her; there is no rape scene upon being beaten by her, and you shouldn't be able to beat her. This Lucifina is just a copy of the one who fought in the Great Monster Wars. But she doesn't recognise Luka, and will attack him on sight.
In the Labyrinth of Chaos, she can be fought as a super boss. You shouldn't be able to beat her in part 1 (like the rest of the super bosses), but it can be done. Through grinding, and exploiting a skill called Vicarious Clara (you can unlock that through the Necromancer Job). Vicarious Clara provides the user with a shield which absorbs three hits, and can be stacked infinitely.
She is one of the harder bosses in the Labyrinth, due to her passive ability to reflect physical attacks. You want all of your characters you bring to the fight to have access to Vicarious Clara. All of them.
Fight her like you would any of the LoC bosses. Including the rest of the super bosses, like Reaper. However, you want to take some other things into account:
- She is the opposite of Micaela. Instead of reflecting physical attacks, she will reflect magical ones. However, holy and dark magic is an exception to this, but you want to avoid using them, due to Lucifina's high resistance to both. Just focus on physical attacks. Since she has a high evasion chance, certain hit helps here. So try using Makina skills and attacks, which are physical based.
- While she may be immune to magical attacks, there are two exceptions. Timewarp Dance and Curse Dance. Timewarp Dance comes from the Seadragon Dancer, while Curse Dance comes from Dancer. Both can be helpful in this fight, as she is weak to time magic and silences.
- Like Micaela, she can inflict party wide ascension, instant death, and seduction. Counter this with Nanabi or Kamuro, who have access to the Fox Geisha race. They can both use anti-death song, which grants immunity to instant death. Or you could just bring a whole party of Minor Chaos, and Ghost race members. Vicarious Clara can block seduction, but a Superstar like Sully or Saki will grant immunity to it through a skill if it bothers you.
- She can inflict burn, freeze, and shock, but Vicarious Clara can block those attacks.
- She can use a skill called Daystar, which does as you would expect it to, it counters all of your attacks for one turn and deals massive damage. Thankfully, the Daystar can be blocked by Vicarious Clara, but it can still proc ascension. And the Fox Geisha grants immunity to Ascension and Instant Death.
- Now, Lucifina has a skill which counters Vicarious Clara very well. It's called Ninefold Rakshasa. Unless the target in question has nine Vicarious Clara shields, it will die. But, it can be dodged, unlike Lucifina's other skills. The Wind Harpy will counter Ninefold Rakshasa as it will increase your chances of evading it. Use Chirp for this.
- Lucifina's self-buff increases her agility, evasion, and accuracy. It's an annoying buff. It means she is more likely to attack before you can, she will evade your attacks that aren't guaranteed to hit and the possibility of her hitting her target with Ninefold Rakshasa increases. To counter this, increase your parties stats. Use certain hit physical attacks, and increase your evasion and agility.
- Since she can be silenced, you should try silencing her as often as possible. It will prevent her from using magical attacks like Daystar, but she can still use physical ones like Ninefold Rakshasa.
I got most of the information from the guide and the video. Both are extremely helpful, and I'd highly recommend you check both of the guides if you're serious about beating any of the LoC bosses.