Oh, so what looked like a piece of wood which I assumed was from the tree that was trapping her is actually some piece of the demon king with a mind of its own.
More importantly, it appears Lucelia had a completely different personality when she was young, which was not demon like at all, and I wonder if having that piece of the demon king stabbed right inside her skull and brain isn't brainwashing her in some way. It's probably also the reason for the anomaly that Sylphy noted regarding Lucelia not abiding by the rules of summoning and getting reset to level 1 - at least when summoned.
Oof, and Sylphy took some huge damage; that arm getting twisted like that makes it seem like the bone was shattered in many pieces. I don't recall her having the means to heal though so I'm curious to find out how that will be sorted out.
It seems like this fight is coming to a close now that we have a clue what needs to be done. I expect that once the stake is removed, Lucelia will be reset as a summon and recover the personality we saw and become another fun companion for the MC.