I had the same problem, so here is the solution. The reason the keyboard/mouse don't work inside the ubuntu 16.04 LXC container is that the xserver-xorg-input-kbd package was dropped, so if you used something like
...
Driver "kbd"
...
Driver "mouse"
...
in your container's xorg configuration - it would not work on ubuntu 16.04.
Instead you should configure xorg inputs with evdev. Since the exact number of event* entries in the configuration file (e.g. /usr/share/X11/xorg.conf.d/10-lxc-input.conf) will depend on what is in your container's /dev/input/, you could use a script to generate one:
#!/bin/bash
cat >/usr/share/X11/xorg.conf.d/10-lxc-input.conf << _EOF_
Section "ServerFlags"
Option "AutoAddDevices" "False"
EndSection
_EOF_
cd /dev/input
for input in event*
do
cat >> /usr/share/X11/xorg.conf.d/10-lxc-input.conf <<_EOF_
Section "InputDevice"
Identifier "$input"
Option "Device" "/dev/input/$input"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
_EOF_
done
Which results in something like: cat /usr/share/X11/xorg.conf.d/10-lxc-input.conf
Section "ServerFlags"
Option "AutoAddDevices" "False"
EndSection
Section "InputDevice"
Identifier "event0"
Option "Device" "/dev/input/event0"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event1"
Option "Device" "/dev/input/event1"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event10"
Option "Device" "/dev/input/event10"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event11"
Option "Device" "/dev/input/event11"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event12"
Option "Device" "/dev/input/event12"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event13"
Option "Device" "/dev/input/event13"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event14"
Option "Device" "/dev/input/event14"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event2"
Option "Device" "/dev/input/event2"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event3"
Option "Device" "/dev/input/event3"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event4"
Option "Device" "/dev/input/event4"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event5"
Option "Device" "/dev/input/event5"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event6"
Option "Device" "/dev/input/event6"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event7"
Option "Device" "/dev/input/event7"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event8"
Option "Device" "/dev/input/event8"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection
Section "InputDevice"
Identifier "event9"
Option "Device" "/dev/input/event9"
Option "AutoServerLayout" "true"
Driver "evdev"
EndSection