yes it is possible to run a complete X11 desktop environment inside a LXC container.
Right now, I do this on Arch Linux. I won't say it's "light" as I haven't gone as far as trying to strip out stuff from the standard package manager install but I can confirm that it does work very well.
You have to install any kernel drivers on the HOST as well as in the container. Such things as the graphics driver (I use nvidia). You have to make the device nodes in dev accessible inside the container by configuring your container.conf to allow it. You then need to make sure that those device nodes are created inside the container (i.e mknod).
So, to answer you question: YES it does work. If I can help any further or provide more details please do let me know.
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In my container...
/etc/inittab starts in run level 5 and launches "slim"
Slim is configured to use vt09:
# Path, X server and arguments (if needed)
# Note: -xauth $authfile is automatically appended
xserver_arguments -nolisten tcp vt09
I am not using a second X display on my current vt, but a completely different one (I can switch between many of thise using CTRL+ALT+Fn).
If you aren't using slim, you can use a construct like this to start X on another vt:
/usr/bin/startx -- :10 vt10
That will start X on display :10 and put it on vt10 (CTRL+ALT+F10).
These don't need to match but I think it's neater if they do.
You do need your container config to make the relevant devices available, like this:
# XOrg Desktop
lxc.cgroup.devices.allow = c 4:10 rwm # /dev/tty10 X Desktop
lxc.cgroup.devices.allow = c 195:* rwm # /dev/nvidia Graphics card
lxc.cgroup.devices.allow = c 13:* rwm # /dev/input/* input devices
And you need to make the devices in your container:
# display vt device
mknod -m 666 /dev/tty10 c 4 10
# NVIDIA graphics card devices
mknod -m 666 /dev/nvidia0 c 195 0
mknod -m 666 /dev/nvidiactl c 195 255
# input devices
mkdir /dev/input # input devices
chmod 755 /dev/input
mknod -m 666 /dev/input/mice c 13 63 # mice
I also manually configured input devices (since we don't have udev in
Option "AutoAddDevices" "False"
InputDevice "Mouse0" "CorePointer"
InputDevice "Keyboard0" "CoreKeyboard"
Option "XkbLayout" "gb"
Option "Protocol" "auto"
Option "Device" "/dev/input/mice"
Option "ZAxisMapping" "4 5 6 7"
The above going in a file /etc/X11/xorg.conf.d/10-input.conf
Not sure if any of that will help, but good luck!