Could be, but I think that there is a better reason for Fiora not liking Lux, here's my theory.
Fiora and Lux are around the same age, Fiora maybe 1 year older, so they may have know each other growing up, but that's besides the point.
Both are incredibly gifted in their fields, but where they differ is where Lux allows her self to be controlled by Demacia and her family, Fiora did the exact opposite, she defied the Demacian ways and is one of the only non brain washed Demacians. She views Lux being controlled by the military as a waste of potential, she thinks Lux can do so much, but she doesn't, she allows her potential to go to waste being forced to serve Demacia's military, but why I think Fiora really hates Lux is because Lux knows shes being controlled and is afraid too do anything about it. (I'm basing this off of Lux's actually depressed self and everything based off of her judgement and Fiora's personality)