[He treats her like a granddaughter would his granddaughter. Occasional treats and old stories of adventures. I mean...]
Being as old as he is, Ryze looks to Lux and does try to at least give her the right amount of respect she deserves for her age and experience, but sometimes, he forgets that and often times ends up going too soft and avoids most serious subjects when speaking with her.
Now, seeing as they don’t really travel together, it would be safe to assume that they meet around Demacia or some Demacian friendly locations, such as Piltover or neutral territories. They’d trade everyday stories and maybe Lux would try to get the old man to show her something new, whether it’s magic or even something he might have found in a far off land. Even ask about his past.
Of course, he does see Lux as a good friend, still innocent and sweet due to age. Over time, he would maybe consider teaching her a bit more about his magic, but for now, we’ll have to wait and see.