I can even leave uTorrent opened with 300kb download rate with no problem, but i can not play LOL i always have random pings.
When you say 'random pings', do you mean lag spikes? I play LoL occasionally and I don't notice a difference between Spotify being open or closed.
Try this: before your next match, open up Spotify and create a playlist entirely of local files, and see if you experience lag on LoL during that playlist. This will help us determine if the bandwidth occupied by streaming is causing your issues with LoL.