First of all, the -d flag causes the server to run in the background. Which is what you want, only you need to use the kill command to stop it. Depending what distro you're on, you need to do something a little different to get the service to start up with the machine. First, you can copy config/lighttpd.conf to /etc/lighttpd/lighttpd.conf. For production, you need to edit it. At least change the number of min_procs and max_procs to a slightly higher number than "1". Change the environment from development to production. Then on Redhat or Fedora(or CentOS), for instance, if you installed from RPM, you could type # chkconfig --levels 35 lighttpd on
and that would cause lighttpd to start up automatically with the machine. This varies by distro as does the default location of lighttpd.conf.
Read some tutorials about it, then give it a try.