Hi.
What you mention me may be due to two things.
1. League of Leguends works with DirectX 9 basis so if you have installed you can present failures.
DirectX error lol is usually because you are missing a DLL file specific.
This is called d3dx9_39.dll. you can download it from this page.
http://es.dll-files.com/d3dx9_39.dll.html
By accessing the website you give download Zip in the bottom right and select your operating system 32 bit or 64 bit.
A Once downloaded unzip and copy the DLL file:
C: \ Windows \ System32
If you ask what remplazas replace and start the game.
2. If it worked, you played quietly and present this error may suddenly be because unmerged a game as there are games that typically install DirectX (dll) required and when desintalarlos these also deleted the DirectX (dll) that they installed independently
Ons that you need to run any game are (are general ons for games, not just for lol)
* Vcredist 2005, 2008, 2010 and 2012
* Xnafx 3, 3.1 and 4
* Dotnetfx 3 and 4
They are needed.
I hope I have been helpful if I run says that costs nothing XD.