Hi!
The communication between the Chromebook and the LXD containers is quite restricted in order to protect the security of the Chromebook from something unexpected running in a LXD container.
Having said that, if you want to run a browser (or other internet application) in a LXD container, and have them use Pi-hole/unbound/etc from other containers, then you can do so. It is possible to direct the traffic from one container to another.
However, if you want your Chromebook to enjoy the love of unbound/pihole and other network services, you could instead get an inexpensive Virtual Private Server (VPS) like the 1-S, install LXD and add unbound/pihole/etc. You need to also add a VPN software like OpenVPN so that the whole Chromebook connects to the Internet through this VPN.