Riot's aware and are working on the 'FPS issues'
My computer can run league at 360 FPS uncapped--- just to illustrate how beast-mode my machine is. It's optimized for professional graphics, 3D processing and video manipulation. Take any videogame and run it in highest quality and watch this beast sail through it.
And then there's League.
The FPS drops have been building up for a few months. 4 hours gaming I'd drop to around 30 FPS... then 3 hours... then 2 hours... now at about 1 and a half hours it's getting down to 10. F-ING. 10 FPS. I patch today and I open it up to check if league's launching atall- 10 at bootup. I restarted my PC and it cleared whatever the blockage was (I assume it's because I had the CLIENT open for a while leaving it to update) but it was back down to that in an hour and a half of gaming (I do have the client set to close during game so it's not limited to the client). Absolutely bloody ridiculous.
I have a work around-- I duplicate my league data onto an external hardrive and run it off that. I have no idea what this is doing or if it indicates there's an issue with my PC, but given it's a common issue and League-specific, I think there's something they can do on their end.