In my opinion its just league causing the issues, they have been having lots of issues with a lot of internet providers, and there for a while i was lagging none stop for like 2 months they have gotten a lot better now but over all that's one of the main reasons why i quit as there servers are always lagging and there will be times where i will be playing rank and i start disconnecting. playing any other game/searching the web i have not had any issues.
One thing you can try is changing your DNS to googles DNS see if it helps you.
Start - Control Panel - Network and sharing center - Change adapter settings - Right click the connection you are using - Properties - Internet Protocol version 4 - Use the follwoing DNS server addresses...