Never fear, I have the solution!
1) Go to your Riot Games installation on your harddisk, usually C:/Riot Games/League of Legends
2) Open the following directory:
rads // projects // lol_air_client // releases // [the highest number]
Delete the following files:
Open the 'deploy folder'
3) Within this deploy folder, delete the following folders/files:
- lib (folder)
- META-INF (folder)
- mod (folder)
- lolclient.exe (file)
- lolclient.swf (file)
- locale.properties (file)
4) Restart your LoL application