Ez has mentioned in this conversation that Luci's former self is of noble lineage, which was the echo he previously received. This much is very true. She received a memory of her name in a previous echo (again triggered through conversation), and her first echo was the mantra "To fight for justice in the name of Demacia," which is a piece of the indoctrination given to students of the Magic Academy as well as parts of the Demacian military to instill allegiance to home and country. She's inferred that it would either reference a person or a place, given the nature of the phrase. Given the context of the quote itself that she has received and, quite honestly, has devoted a lot of her personal time trying to figure out, and having remembered her name, I feel it's easy to see a line drawn to the two points through this.

That said, in canon Lux is from the house Crownguard, one of the largest and most decorated houses within the kingdom of Demacia. There's a bit of a write up of the LoL wiki page, as well as information about the kingdom of Demacia.