Laptop under $400 that can run LoL at 60 fps?

I know it's extraordinarily cheap, but the laptop I'm currently playing on was $300 and I get 60 fps and have literally never had an issue. Not even an i3 equivalent processor and the graphics card is absolutely garbage.

So, if anyone who is tech savvy could search around on this page (I know nothing about processors, graphics cards, viability, etc.), I would appreciate it. What I need to know is this: Can it run League of Legends with 60 fps (or close to it) and have little to no issues. I know it's feasible, I'm only asking for someone smarter than I on the subject to assist me.

PS: Feel free to add things to make the search slimmer (e.g., i5 processor, 1080p). Refurbished is fine as well.

http://www.bestbuy.com/site/searchpage.jsp?cp=1&searchType=search&_dyncharset=UTF-8&ks=960&sc=Global&list=y&usc=All%20Categories&type=page&id=pcat17071&iht=n&seeAll=&browsedCategory=pcmcat138500050001&st=pcmcat138500050001_categoryid%24abcat0502000&qp=null%5Ecurrentprice_facet%3DPrice~%24250%20-%20%24499.99&sp=%2Bcurrentprice%20skuidsaas