For our Mac players, please try the following:
Navigate to Go.
Click on Applications.
Control + Click (or "Right-click") League of Legends PBE.
Click Show Package Contents.
Navigate to ...\RADS\projects\lol_air_client\releases\[latest version]\deploy\bin\mod
Delete the rds folder.
Launch League of Legends.
Note: This only applies to this specific PvP.net FATAL ERROR 0001 (other FATAL ERRORs may not be fixed when following the above steps)
Also, [latest version] refers to the folder titled 0.0.0.69, 0.0.1.37, 0.0.1.38, 0.0.1.41 or higher.