Hi Tim, 

I found a workaround to use nvidia driver with lightdm + gnome-shell. 
WIth nvidia-331 driver, lightdm and gnome-shell, in "System Settings" (gnome-control-center) --> "Displays", I can still see two displays "Built-in DIsplay" and "Unknown Display". This is the same to "Intel driver" situation. All the layout problems I met so far can be fixed by turning off "Unknown Display" in gnome-control-center. After turning off the "Unknown Display", gnome-shell works perfectly. And then I tried to launch "nvidia-settings", it shows "CRT-0 Off". I am thinking the "Unknown Display" might be refer to CRT-0 (VGA-0) ?

Note: I tried to configure "nvidia-settings" layout, it does not work. In "nvidia-settings", It only has CRT-0. (CRT-0 is using "X Screen 0" configuration. and in "X Screen 0" --> "X Server XVideo Settings", it shows CRT-0 is the same as VGA-0. Hopefully, this paragraph is not confusing you.) 

PS: I am not sure how to upload multiple files at once or even if that is possible in launchpad. I will upload three screenshots to make my words more clear. 

nvidia-builtin-display.png is a screenshot which shows built-in display setup in gnome-control-center before turning off "Unknown Display". 
nvidia-unknown-display.png is a screenshot which shows unknown display setup in gnome-control-center before turning off "Unknown Display". 
nvidia-turnoff-unknown.png is a screenshot after turning off "Unkown Display". You can see that the layout looks perfectly by turning it off. 

I have no idea why both intel driver and nvidia driver think I have an extra "Unknown Display" VGA-0 or CRT-0. 
In the end, I will show the final "xrandx -q" output after turning off "Unknown Dispaly":

$ xrandr -q
Screen 0: minimum 8 x 8, current 1366 x 768, maximum 8192 x 8192
VGA-0 connected primary (normal left inverted right x axis y axis)
   680x384        60.0 +
   1366x768       60.0  
   1360x768       60.0  
HDMI-0 disconnected (normal left inverted right x axis y axis)
LVDS-1-0 connected 1366x768+0+0 (normal left inverted right x axis y axis) 293mm x 165mm
   1366x768       60.0*+
   1360x768       59.8     60.0  
   1024x768       60.0     60.0  
   960x720        60.0  
   928x696        60.1  
   896x672        60.0  
   960x600        60.0  
   960x540        60.0  
   800x600        60.0     60.3     56.2  
   840x525        60.0     59.9  
   800x512        60.2  
   700x525        60.0  
   640x512        60.0  
   720x450        59.9  
   640x480        60.0     59.9  
   680x384        59.8     60.0  
   576x432        60.1  
   512x384        60.0  
   400x300        60.3     56.3  
   320x240        60.1  
VGA-1-0 disconnected (normal left inverted right x axis y axis)
HDMI-1-0 disconnected (normal left inverted right x axis y axis)
DisplayPort-1-0 disconnected (normal left inverted right x axis y axis)
  1366x768 (0x46)   69.3MHz
        h: width  1366 start 1425 end 1464 total 1472 skew    0 clock   47.1KHz
        v: height  768 start  773 end  782 total  785           clock   60.0Hz
  1360x768 (0x48)   72.0MHz
        h: width  1360 start 1408 end 1440 total 1520 skew    0 clock   47.4KHz
        v: height  768 start  771 end  781 total  790           clock   60.0Hz
  680x384 (0x5c)   36.0MHz
        h: width   680 start  704 end  720 total  760 skew    0 clock   47.4KHz
        v: height  384 start  385 end  390 total  395           clock   60.0Hz

The only difference I can find here is that:

VGA-0 connected primary (normal left inverted right x axis y axis)
   680x384        60.0 +

Before turning off "Unknown Display", it was:

VGA-0 connected primary 680x384+0+0 (normal left inverted right x axis y axis) 0mm x 0mm panning 1366x768+0+0
   680x384 60.0*+