Random fps spikes in games

Hello,
I have been having for about the last 7 months a really bad problem with lag on my computer with some games, and none lag whatsoever with others... So before my lag started i use to play a game called League of Legends and recently my friends started playing it so i wanted to get back into it, But i cant because for the last 7 months i havnt been able to play a lot of my games. Now if you know what League of Legends is you would know it obviously doesnt have as high graphics as a game such as warcraft which are pretty identical games, YET i can play warcraft without any lag whatsoever not even a random lag spike for hours of straight gameplay. I honestly dont know what the problem is and i just wish i could get this fixed already. Id appreciate any replies that can help and here are my system specs (I dont know too much about pc's so ill post the specs i know how to find?)

EDIT: I forgot to mention that the lag lasts for about 6 seconds at a time where it drops to 6fps and then it goes back up to around 70fps for 10-20 seconds and then drop back to 6 and repeats this with no end  

AMD Athlon(tm) dual X4 620 processor
2.60 GHz, 3.12 GB of RAM
Service Pack 3
Nvidia GT 240 Graphics card
500GB Hard drive space

Thanks for reading i really hope someone out there can help me