I installed lighttpd (as a server for phpmyadmin) on two machines with the same result. The server initialized at boot and with restarts with an "ok" but it wouldn't serve anything (web pages or php). The install for phpmyadmin gave options for which sever to configure, and I had indicated lighttpd. Checking the error logs I discovered that the php5-cgi package was required by lighttpd. I installed the package and all is fine now.

What I'm wondering is if we should give feedback on this? It seems if phpmyadmin installs with an option to configure lighttpd, the required packages should be included with the install.

you could file a bug report against that package.