So today for the first time i have encountered the problem with "Cannot load direct3d" and i saw here on the forums that some people had this problem as well.
I don't know if this will help anyone but if there is a chance it might ill post it.
As i said today for the first time i encountered this problem and at first i was frustrated,after a few tries of starting up LoL i decided to close all of the programs i had running in the background to reinstall some drivers.
The programs that i closed were iTunes(an older version) and Starcraft 2.
Then while i waited for the drivers to download i tried to start up LoL and it worked,without installing anything new.
I tested it once again and ran Sc2+iTunes and tried to start up LoL and the same direct 3d message popped up.
I'm not sure why these would interrupt the game in any way but for me its the case.
If your having the same problem try checking or close the programs i listed or there might be others that cause this.