Hello,
I've recently bought an AOC e1649Fwu USB external monitor with DisplayLink and was unable to play League of Legends on Win7 64-bit. Solution for Win8 posted on DisplayLink pages didn't work for me. But I found a way. You have to configure League of Legends to run in a window. It seems, that directx has problem determining what is fullscreen if there is DisplayLink driver present in the system. So to run League of Legends you have to do this:
1. Navigate to your League of Legends install folder (default is C:\Riot Games\League of Legends\Config\)
2. If there is a game.cfg file, edit it as follows:
under [General] section find line "Windowed=0" and change it to "Windowed=1"
If there isn't any game.cfg file, download mine and copy it to the config folder.
3. Run a game, go to tutorial (it is easy to quit) and change the resolution via in-game menu. You have to do it this way, because the game recognizes only a pre-defined resolutions.
To change window resolution you must enter a game (it is not possible from launcher) and press Esc key after the game loads.
In Options menu click on Video button. Select a suitable resolution from Resolution menu.
Do not change the Windowed Mode option or you will be at the beginning again!
With resolution selected, you can quit the tutorial (there is no ban for exiting a tutorial).
I hope this works for you.