Docker inside LXC adds not only the overhead they’d individually add — probably not significant enough for it to matter in a homelab setting — but with it also the added layer of complexity that you’re going to hit when it comes to debugging anything. You’re much better off dropping docker in a full fledged VM instead of running it inside LXC. With a full VM, if nothing else, you can allow the virtual networking to be treated as it’s own separate device on your network, which should reduce a layer of complexity in the problem you’re trying to solve.
As for your original problem… it sounds like you’re not exposing the docker container layer’s network to your host. Without knowing exactly how you’re launching them (beyond the quirky docker inside LXC setup), it is hard to say where the issue may be. If you’re using compose, try setting the network to external, or bridge, and see if you can expose the service’s port that way. Once you’ve got the port exposure thing figured out, you’re probably better off unexposing the service, setup a proper reverse proxy, and wiring the service to go through your reverse proxy instead.