Note that lighttpd is the only web server officially supported by Pi-hole.
So you are running a bare metal Pi-hole with its lighttpd web server active and configured for a custom port.
In that case, Pi-hole's UI should be available at http://pi.hole:<custom-port>/admin - there would be no immediate need to involve a different webserver.
Nevertheless, as mentioned, based on your intention, you should be able to configure your Caddy webserver to point HTTP requests to be handled by lighttpd's port instead of having Caddy handling them.
This would essentially be a question of how to configure Caddy, so you may want to consider consulting Caddy's community support as well.
From your description, your second observation may constitute a different issue altogether (click for quote details):
I'm going to split that into a separate topic.