From what I've seen magic can come from several sources. And that's when you have to DEFINE what magic you're referring to.
There's magic that stems from items or lands of immense magic potential, and thus grant the user powers, be it a blessing or a curse. Two examples would be:
- Runes from the runewars
- Curse of the Shadow Isles
Then there's inherent magic or stuff that's passed down by bloodlines.
This was mentioned in Ryze's lore when he says "The magic is in your blood"
--This is what I imagine Lux went through. A exceedingly thin bloodline of magic that was awakened through a experience. An alternate idea is that magic is intrinsic in EVERYONE's blood but it's exceedingly thin, going back to the origin of the world itself, which allows self awakening, rare as it may be.
While on the other hand there are others with thicker bloodline from societies attempting to keep magic in their bloodline stronger- something that's occurred with nobility or other such "High" titles in history in the real world.
-- This idea is somewhat supported by the sheer power of the magic users in the past comparative to the more recent magic users. The idea that the amount of "mana" or magical talent that they had was much higher in say the time of Shurima, then in the Noxus X Demacia era. This shortcoming however is argualy made up by the developments in magic development.
An example of this idea is take Ryze, who -at least it seems- uses compressed mana with the assistance of runes to crush people, or Xerath who does similar, to more "Current day" champions such as lux or taliah or even swain who have a lesser amount of power, but have their magic shaped into an element or property which allows it to do more damage.
This idea would also support the idea of innate talents being in all people which allows for people like Kat who have talents other then magic.
However it's also somewhat flawed by the existence of people without mana - Kat/Garen albiet it could just be argued that their magic talent was excessively low.
On the other hand it would also explain why champions as, say, Dairus have mana. That mana is something that is part of them, and although they are unable to use it to, say, blast people away, it can help them use more strength or power then natural.
I'm not going to go much further because I'm about to go do something but yeah. That's my take on magic in Runeterra.