Lux and Nox have specified owners (Lux can only be held by a creature of true light, and belongs to Lily anyways. Nox can only be wielded by a creature of darkness (Someone who has powers or has a connection to dark magic such as curses). That does include Axel.

The other four are up for grabs, but if held by someone wielding the opposite element, there's a high chance it would backfire (Lily would have trouble wielding Ignis, for instance, because of her connection to water)