This sounds like an issue with the connection between your pc/internet and the league servers
So here are a few key points
What kind of FPS and Ping do you have normally? (before this started)
Has your FPS or Ping changed since this started?
What kind of internet connection/speed do you have?
Is the connection between your internet router/modem and pc wired or wireless?
Have you tried uninstalling and reinstalling the game to see if the issue persist?
I ask these because there is a possibility of one of two things.
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A corrupted game filed that the repair tool is unable to find and fix. There is a limit to what it can do, so if a file get corrupted and the repair tool doesn't fix it, or see it, the problem remains. Doing an uninstall and reinstall might fix this problem.
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There is an issue between the connection of your pc/internet and the league servers.
The first one is a bit easier to fix.
The second one is a tad harder.
Get the info for these questions and post the answers and we shall see what else can be done.