Try this;
Navigate to your config folder and open the Input.ini with notepad (C:\Riot Games\League of Legends\Config\Input.ini)
Add in the following lines of code:
[GameEvents]
evtPlayerMoveClick=[Button 1]
evtPlayerSelectClick=[Button 2]
If [GameEvents] already exists, just add the last two lines below it (That would be if you already have changed current keybindings inside of the game).
That should get your left-click and right-click reversed! :-)
If it doesn't work, afterwards, try doing this;
Close League.
Go to C:\Riot Games\league of Legends\RADS\projects
Delete the Delete the lol_air_config_na folder
Restart the client to redownload it.
Log into NA
Go to C:\Riot Games\league of Legends\config
Delete PersistedSettings.json, game.cfg and input.ini
Create a custom game to test it.
If you still can't get it, throw up a thread on the Help & Support board.