This a great mod, but I've been having this error ever since the Financial Districts game update. Similarily with UUI and LOM.
The Mod G:\Games\Steam\steamapps\workshop\content\255710\2781804786 [GameAnarchy.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll, GameAnarchy.resources.dll] has caused an error [ModException]
Details:
System.IO.IOException: Sharing violation on path G:\Games\Steam\steamapps\common\Cities_Skylines\Cities_Data\GameAnarchyDebug.log
at System.IO.FileStream..ctor (string,System.IO.FileMode,System.IO.FileAccess,System.IO.FileShare,int,bool,System.IO.FileOptions) <0x00959>
at System.IO.FileStream..ctor (string,System.IO.FileMode,System.IO.FileAccess,System.IO.FileShare) <0x00042>
at (wrapper remoting-invoke-with-check) System.IO.FileStream..ctor (string,System.IO.FileMode,System.IO.FileAccess,System.IO.FileShare) <0x00078>
at MbyronModsCommon.ModLogger.OutputPluginsList () <0x000bd>
at GameAnarchy.Mod.OnLevelLoaded (ICities.LoadMode) <0x000cc>
at (wrapper dynamic-method) LoadingWrapper.LoadingWrapper.OnLevelLoaded_Patch10 (LoadingWrapper,SimulationManager/UpdateMode) <0x00114>

I have to delete the GameAnarchyDebug.log before every game load to play the game.
I see others having similar issues with LOM also. I've tried re-installing both Steam and CS.