Please don't just say get a better computer, I know a lot of friends who don't really have the option to get an amazing gaming computer. That doesn't mean they can't play league, Riot should be able to cater to these people so they can play the game and have just as much fun as people with supercomputers.
Turning down the graphics is the first obvious solution, if it still isn't fixed some resolution changes can be made but I think that there should be a way to turn off some of the environment effects like those pesky bats by the golems that could maybe help people run the game just a bit faster.