There are a lot of open-source game projects that have started over the years. Some have turned into fully-completed games, but they are very few. And those generally are not asset-heavy, which I suspect a League of Legends-style game will be.

This could make it, but I wouldn't be placing money on it.

I think if I were gonna try and do that, I'd aim for making the game playable with what amounts to just about placeholder assets.

The engine side is the easier part. You've got a number of people who have done engine reimplementations of a number of commercial games that can play the original game using the original game's assets. But getting a game with original assets is hard.