I'm having the same issue, as well. Previously, I ran the game with 'Medium-High' graphics, full screen, no v-sync, 60 fps capped (can reach 120). Since the patch, my fps tends to linger around 20-30 fps but can drop to as low as 5. I've tried:
- repairing
- re-installing league
- lowest graphics settings, lowest resolution, all fancy glitter stuff off
- going borderless
- setting league client to 'high priority' or whatever through task manager
- running league client as administrator
- prioritizing performance on windows
- updating windows
- re-installing my graphics drivers
The latter-most gave me momentary joy and 80 fps the following game; however the fps drop issue returned again mid-game and persisted. Re-installing the drivers again didn't yield the same results. I'll try switching to legacy client now since I'm desperate. :') I'm a Windows 10 baby, btw, if it matters.
EDIT: Legacy client tried, FPS still booty.