by the look of the recommended ( not the minimum ) requirements to play this game
you need a 3ghz processor , the HP Pavilion 15-n268sa has a 2.1ghz processor so given that i would say no ,
check these specs on the link , do your research by checking the laptop specs and you will find a laptop that meets those requirements
You'll have a tough time maxing out games with that laptop, for a laptop to run games well you need to up your budget by a few hundred. A starter gaming laptop is around $700 with mid range models $1,000-1,200
The A10 CPU/Video is OK for lower resolutions and video settings or for older games. It will run Half Life 2 very well for example.
The laptop seems to have an ok spec. The dual graphics in it are a good sign when it comes to gaming. Also, League of Legends would run on a toaster, so I think you'll be fine in that aspect, and so will most source engine games. Don't expect to be maxing games out, but it will run just fine. Also as an alternative, I would recommend picking up a desktop for about the same price, as it will have a much higher spec, and a desktop at that price will be able to play games from today, BF4, COD, Titanfall, etc.