Well, if they made a movie, a lot of fans would be extremely unhappy. We all know how gamers react to being unhappy, as well. The reason being that League has over 100 champions now, and to do a movie that includes all of them would be impossible. So, Riot and the movie company would have to pick 2 or 3 champions to make the main characters, and tell a story revolving around them. Sure some of the other champions would be in too, but for the most part they'd be in minor roles, and some wouldn't appear at all. So how would Riot pick which champions to make a story about? The fanbase is so diverse in who they like, a lot of people would be unhappy with the final product, regardless of how well it's actually made.
Alternatively, they could do a movie revolving around a Summoner, which would probably work better so long as they were honest up front about it and the fans didn't go in expecting to see their favourite champions as the stars. However, the finality of a movie resolution might not mesh well with the ongoing lore of a video game. Let's say Noxus were being sneakysnakes and conspiring against Demacia, how would it be resolved without effecting the game?
The best way to do it would be to make a movie showing some past event in the lore, I think. It would be interesting to see a story we've only read about come to life on the screen.