It also counts as a Good Costume Switch. She could possibly Letting Her Hair Down(and/or get an Important Haircut) and ditch the school uniform for casual clothing.
This brings up two possibilities:
1) Lucy is a member of Luz's family from another city.
2) She's a version of Luz from another dimension, presumably an alternate "The Owl House" world.
It seems odd that she A: is related to such a distinctly different being like the Warden and B: that someone as important as him would come from the 'Nothing' class. He probably adopted her when she graduated to being a 'Weak'.
- Confirmed. Warden Wrath is her adopted father; her birth father is Alador Blight who raped her mother Persephone Brae using mind magic by Odalia.
Because why not.
Between her association with train, dogmatically self-serving nature, and refusal to compromise her beliefs in "survival of the fittest", she or John Galt might be an interesting example of a 'hopeless passenger' and a contrast to Boscha.