There are network operations in progress and you are surely not the only one who's getting the annoying RADS error
Go to C:\Riot Games\League of Legends\RADS\system
Open the system.cfg file with notepad and copy paste one of the following lines depending on what region you have :
DownloadPath = /releases/live
DownloadURL = l3cdn.riotgames.com
Region = NA
DownloadPath = /releases/live
DownloadURL = l3cdn.riotgames.com
Region = EUW
DownloadPath = /releases/live
DownloadURL = l3cdn.riotgames.com
Region = EUNE
save the file and try to re-open your launcher. it should now start patching
Hopefully this works for you