Yes you can do nested LXC containers and despite the 1st comment there are times and use-cases where Nested containers are certainly useful. See Stephane Graber's 10 part LXC blog but in particular the section Container Nesting -
Stephane Graber's 10 part series on LXC
use-cases: Suppose you want a mult-tenant LXC environment. Create 1 Master container for each person or organization making sure to enable Nesting by adding the 2 cmds to the LXC container config file. Next in each Master container create your nested sub-containers where you install the apps, desktops etc that each group requires. NOTE that whereas the default network for the Master containers will be 10.0.3.x the nested containers will be 10.0.4.x by default (you can change either if you need to).
What is the biggest advantage I 've had using Nested LXC? If you lxc-stop the Master container and lxc-clone it.. you clone not only the Master but all the sub-containers... this is handy for quick backups. This approach is also handy if you ever want to do LXC live migration w/CRIU. When you migrate one of the Master containers to another Machine... you are actually migrating it and all nested containers as well.
Lastly, for a cool example of LXC nesting use Stephane Graber & others built a simulator for "The Internet" using LXC, BPG & OSPF all in 1 LXC container. Inside that 1 LXC "master or parent" LXC container there are 512 nested LXC containers each running Quagga for BGP/OSPF routing. Together those 512 Internet "nodes" simulate the Internet. This implementation was used at the 2014 NSEC security conference for all the attendees to experiment with security in the Internet.
The source for this is on Githug at:2014 NSEC LXC simulator for The Internet github code