This kind of problem is almost always a driver issue. I have experienced similar issues myself. To start, make sure your drivers are completely up to date by checking the AMD driver's site here.
And make sure directX is up-to-date by checking the Microsoft page here.
Now, sometimes the drivers themselves can be fine, but their software is trying to optimize league but backfiring. League is pretty good at optimizing itself, but does NOT play nice with other programs that try to optimize it. Reset your drivers software to default and see if it helps:
#CATALYST CONTROL CENTER
- Right-click on your desktop and select Catalyst Control Center (also called VISION center).
- Select Preferences.
- Click on Restore Factory Defaults.
If you are still experiencing issues, try playing around with the V-Sync options in the Catalyst Control Center/Vision Center. Generally having it turned on in the control center but OFF in league itself tends to be the best. But try different V-Sync settings to see if any of them improve performance. If they don't help, remember to reset to default so that it doesn't hinder further fixes.
If none of the above work, Riot Support has a handy Low Frame Rate Troubleshooting Guide that goes over other possible fixes one by one.
If all else fails, you can always get help directly from Riot by sending in a Support Ticket
Important:: Before doing so, make sure to run the Hextech Repair Tool to gather logs, then attach these logs to the ticket. This is important as it gives riot all the info they need to help you.
