hello there as a fellow player of league of legends and proud owner of a MSI ge62 laptop i can attest that league will run on medium to low settings on the integrated graphics chip which is the intel hd4400 i did notice however my computer ran hotter than when i used the dedicated graphics gtx 965m so you can run league of legends of an integrated graphics chip like an intel hd 4000 series or higher so there fore finding a laptop in your price range that can play it should not be too big of a problem but it will probably put alot of strain on the integrated graphics if you dont get a laptop with a dedicated graphics card which is what i would recommend but those start at the 600$ price range if your lucky hope this helps good luck on...