I tried Dota 2 on a G2030 and the performance was sub-par. Sometimes when loading a game it would crash when everyone's heroes (champs) spawn. It also lagged a lot during larger team fights.
It was not a GPU bottleneck in anyway. My CPU was constantly at 95-100% and the GPU was sitting at 30-40%.
LOL might have lower graphical requirements, but the CPU requirements might be very similar to Dota 2.