Still poking around on this, I decided to start with my drivers.
When I run, nvidia-smi, I get the following:
+------------------------------------------------------+                       
| NVIDIA-SMI 331.79     Driver Version: 331.79         |                       
|-------------------------------+----------------------+----------------------+
| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |
| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |
|===============================+======================+======================|
|   0  GeForce GTX 560    Off  | 0000:01:00.0     N/A |                  N/A |
| N/A   41C  N/A     N/A /  N/A |    131MiB /  2047MiB |     N/A      Default |
+-------------------------------+----------------------+----------------------+
                                                                               
+-----------------------------------------------------------------------------+
| Compute processes:                                               GPU Memory |
|  GPU       PID  Process name                                     Usage      |
|=============================================================================|
|    0            Not Supported                                               |
+-----------------------------------------------------------------------------+
Should I be concerned that it says off next to my card name?
Should I try updating to the more unstable 337 driver?
Am I wasting my time trying to run League in wine? (I want to help, but do I have unreal expectations)
Furthermore, I started running the game in an emulated desktop at 1024x768 res. It didn't help my in game framerate at all. Also my out of game shop is crashing my game, but that's a known issue that seems to have a solution (somewhere).
Thanks!