The lag makes the game unplayable

I've been playing league for about half a year now and the first 3 months i have no problems with the game. I've been playing it on the same computer, however when I try to play it now it lags like crazy. It plays normally for about a couple of minutes and then the MS spikes up to 400 for a a couple of seconds and then plays normally again. This becomes a big problem when I am attacking enemy champions. When I play Fiora it's impossible to parry their attacks, and when I am Zac I can't land on them when I jump. Is there a solution?