I have pretty bad computer specs and im around 50-70fps at all times. The fps only drops to 26 or something when there are like 4 waves of creeps stacked up and I go to clear them. Do you have that kind of FPS all the time or just when the place is crowded for example in teamfights or when many creeps are around?
Can you be more specific about when your client is dropping in FPS?
Though I would try to repair it first. Awhile ago I was having issues with random FPS drops (from a stable to 60 to roughly 2) so I uninstalled and reinstalled LoL. I didn't really think about repairing. Probably would have worked I just forgot about it.
But, my client prior to uninstalling was ~1.5gigs. I reinstalled and it was 3gigs. idk how the game was running with half of the files, but the FPS drops stopped happening afterwards.