At first, didn't like Luce, she was arrogant and abused her role to a point of trying to make Houma to serve her. Know your place.
But she performed her role with surprising confidence...
Luce gave plenty of good advices, but Houma is stuck with low self esteem mindset, but at least tried to help her not like her "friend" Tendou.
That said, it would be a good idea if both of them bailed together, maybe to where she was enslaved or as she has some knowledge of the world, basically anywhere as far away from the kingdom.