Uh, i don't wanna break ur bubble, but NO, it will not run League, you'll be lucky if you will be able to move in-game, you will be able to have the client open, but i don't think it'll be able to "Play" League. Laptops like these are productivity laptops, cheapies for school and microsoft word and such, or just web browsing.
You'll have to raise your budget considerably if you want to game on a Laptop, you could get a really cheap desktop and actually play League though, prolly only run you about 300-500$ish to play League without any issues. Before i bought my new PC i had a crappy little $500 desktop that worked fine for League, but when i wanted to play other games i had to upgrade xD.