See the problem I have with the idea of a League movie/show is that the lore just doesn't lend itself to that kind of format. League does not have a singular story; it's a bunch of different stories happening in one world. There are so many possible conflicts and viewpoints to focus on that it's impossible to wrap it together into a single plotline. Like, say Lucian were chosen as the protagonist. The whole movie/show would revolve around his conflict with the Shadow Isles, and only characters who have been involved with that storyline (most undead champs, Illaoi, Miss Fortune, etc.) would make an appearance. Alternatively, you could make it about Nunu and Willump as they journey across the Freljord, and see how they contribute to the all the war and chaos going on in the tundra.
Simply put, there's too much to focus on for a single movie to cover, and 1-2 episodes of a TV show isn't nearly enough time to do a champion's tale justice. I don't deny it's POSSIBLE, but I think League just works better with the written/comic book format that it's gone with so far.