1. Try running as an admin by right clicking on the executable and selecting "Run As" and "Administrator", or by using the lol.admin.launcher.exe

2a. Delete everything inside the your RADS downloads folder (Default Path is, C:\Riot Games\League of Legends\RADS\downloads) AND
2b. Delete everything inside your RADS solutions folder ( Default Path is, C:\Riot Games\League of Legends\RADS\solutions)
2c. Restart your computer and repatch

3a. Delete the lol_air_client folder in your RADS projects folder (Default Path is, C:\Riot Games\League of Legends\RADS\projects) AND
3b. Delete the lol_air_client_config_na and the lol_launcher folders inside the RADS projects folder.
3c. Restart your computer and repatch