So I have this issue living in a house with 5 people with around 5 computers that can play LoL but the problem was 3 of them are Mac's... Don't ask why I absolutely hate Mac's but people insist that their silver shine is somewhat amazing.
Anyways back about a year ago they shutdown the mac client that you could get through various sorts people and tinkering had to be done a bit with the files and for anyone who played 50% or more games on the mac they had a free champion bundle... Anyways just to get to the point here's the link for people who have Mac's and hate their life when friends say you're sad for not being able to play LoL
Link: http://boompje.net/forum/index.php?action=main
EDIT: The client is currently in beta but the game after doing the changes to your video or whatever you have to do runs very well.