Does garen have some small amount of the same power as lux?

Honestly I can't find any lore on his ult, but the idea that it deals magic damage, and the concept that it does share the same color pallet as lux's powers does make me wonder if this artistic design was related to lore?

if magic runs in the family, My theory is that maybe this magic is tied to their lineage, with requirements of intense focus, whereas lux shows the ability to hyperfocus on everything (She seems to be utterly hyperactively aware of things, which would in fact lead to higher tactical abilities and therefore fitting her character) to a degree that others dont always understand what she's doing, my curiosity is if garen has that ability as well, where his focus is much more limited to justice and martial honor.

In essence garen can only focus his magical abilities in his ult when he is determined, and in his Q to a lesser extent (Silence), though he is much more reliant on his martial prowess and skill, unaware of his magical abilities

This would make lux's special traits out to be her intellect instead of her magic, thus focusing more on her as an individual character, giving her better prowess and in my best opinion, a much richer character... But it also enriches garen's story as an anti-magical knight who has to come to terms with the idea that he might contain said powers. And i'd have to wonder how this would put them at odds with Another anti-magical champion

Now i'm getting ahead of myself in theoretical plotlines involving a sort of... aristocratically arranged marriage with vayne going horribly south as garen has to chose between his virtues, and where he might be forced to protect his sister from a wife he doesnt really love (That wouldn't love him either)