Hi Tim, 

Sorry about the late reply. I was sick.  I tested with the following packages:

$ dpkg -l | grep -i mutter
ii  gir1.2-mutter-3.0                         3.10.4-0ubuntu2                                     amd64        GObject introspection data for Mutter
ii  libmutter0c                               3.10.4-0ubuntu2                                     amd64        window manager library from the Mutter window manager
ii  mutter                                    3.10.4-0ubuntu2                                     amd64        lightweight GTK+ window manager
ii  mutter-common                             3.10.4-0ubuntu2                                     all          shared files for the Mutter window manager

$ dpkg -l | grep -i nvidia
ii  bbswitch-dkms                             0.7-2ubuntu1                                        amd64        Interface for toggling the power on nVidia Optimus video cards
ii  libcuda1-331                              331.38-0ubuntu6                                     amd64        NVIDIA CUDA runtime library
ii  nvidia-331                                331.38-0ubuntu6                                     amd64        NVIDIA binary driver - version 331.38
ii  nvidia-331-uvm                            331.38-0ubuntu6                                     amd64        NVIDIA Unified Memory kernel module
ii  nvidia-libopencl1-331                     331.38-0ubuntu6                                     amd64        NVIDIA OpenCL Driver and ICD Loader library
ii  nvidia-opencl-icd-331                     331.38-0ubuntu6                                     amd64        NVIDIA OpenCL ICD
ii  nvidia-prime                              0.6.1                                               amd64        Tools to enable NVIDIA's Prime
ii  nvidia-settings                           331.20-0ubuntu8                                     amd64        Tool for configuring the NVIDIA graphics driver

Case 1: lightdm, gnome-shell --replace in lxde
    First attempt: the user is forced to logout. I am not sure what exactly happens. maybe the X server gets killed and restarted?
    Second attempt: it kinda works. I don't really see the top bar of gnome-shell. But when I click "shutdown" button, I can see the top bar of gnome-shell with weird layouts. I think this might because nvidia driver does not detect and setup my monitor correctly somehow. Please check the screenshot files: gnome-shell-replace-lxde.png and gnome-shell-replace-lxde-shutdown.png. 

Case 2: login to gnome-shell directly from lightdm
    This kinda works. The layout of the monitor is still crazy. Again, nvidia driver does not setup my monitor correctly. Please check the screenshot files: lightdm_gnome-shell.png and lightdm_gnome-shell2.png

$ xrandr --listproviders
Providers: number : 3
Provider 0: id: 0x28b cap: 0x1, Source Output crtcs: 2 outputs: 2 associated providers: 1 name:NVIDIA-0
Provider 1: id: 0x45 cap: 0x2, Sink Output crtcs: 2 outputs: 4 associated providers: 1 name:modesetting
Provider 2: id: 0x45 cap: 0x2, Sink Output crtcs: 2 outputs: 4 associated providers: 1 name:modesetting

Case 3: switch to gdm
    gdm can not be started. black screen. 

Note that: I can not use intel card by "sudo prime-select intel" anymore. I have to "sudo apt-get purge nvidia-*" to make my intel card work again.