Once of the possible solution is to rename these files.
These files can be found here (The path might slightly different)
C:\Riot Games\League of Legends\RADS\solutions\lol_game_client_sln\releases.0.1.45\deploy
Raname these files to something else eg
LogitechGkey.dll -> AAALogitechGkey.dll
LogitechLed.dll -> AAALogitechLed.dll
This may resolve your issue.
You need to do after every game update.
Enjoy your game!