Laptop that can run most games at 60 fps?

I've been looking to get a laptop that can run casual games like LoL, Minecraft, and various Steam games at 60 fps. I have a Lenovo G500s and it's been slowing down a lot recently. My budget would be under 800. I don't really care about the weight, screen, or anything like that. Also, I don't know many computer related terms.

Quote:- I have a Lenovo G500s and it's been slowing down a lot recently.
Reply:- Computer hardware don't slow down PERIOD, Have you not learned anything yet, It's the operating system (WINDOWS) that slows down
Research what the worlds fastest real time operating system is, why Linux runs the worlds fastest computers, Why Valve (Stream) use Linux

I'd go for another Lenovo if you're comfortable with the brand. They make some pretty good laptops in that price range that could be used for gaming on the games you've mentioned.