I also had this happen with my Avast. It is identifying a specific file in LoL as a virus. I, like most of you, had the "F#$K!" response and deleted the file. Now league will not run properly. I get the "Fatal Error-0002" ErrorID:2032.
All ya gotta do is completely uninstall and reinstall with AVAST SHIELDS OFF. All shields just to be safe. I assume doing something along those lines for other antivirus software should do the trick. After download is complete, turn the shields back on. Avast will continue to think the file is a virus which Riot will have to fix i guess. So dont expect anything soon.