Running Ubuntu Desktop in LXC/LXD on top of Ubuntu Server

Yes it is possible with LXD.

I have my custom LXD Image server. Please do the following:

sudo lxc remote add codedream lxdimage.codedream.ml --public 
sudo lxc launch codedream:ubuntu1604-kodhe-xfcedesktop my-desktop -c "security.privileged=true" -c "security.nesting=true"

Or if you prefer unity desktop:

sudo lxc remote add codedream lxdimage.codedream.ml --public 
sudo lxc launch codedream:ubuntu1604-kodhe-unitydesktop my-desktop -c "security.privileged=true" -c "security.nesting=true"

Also now have ukui:

sudo lxc remote add codedream lxdimage.codedream.ml --public 
sudo lxc launch codedream:ukui my-desktop -c "security.privileged=true" -c "security.nesting=true"

After, install NoMachine, and connect to lxd container by IP and port 4000. Username=kodhe, Password=1. To view IP:

sudo lxc list my-desktop

(Not definitely true:)That won't work!(/Not definitely true) What would work though, is doing it the other way round: install the Desktop on your machine and then use LXD to run the web server.

Also, if you have a current NUC box, you should have processor virtualization and could run KVM. I'm not familiar with that, but it seems your chances are better with a true VM solution...