Lighttpd version "lighttpd-1.4.59" from ports "quarterly" install its default configuration file, with the "var.state_dir=/run" which is not a valid/default path on FreeBSD.
this prevents the lighttpd to start.
2021-06-16 13:58:37: server.c.1270) opening pid-file failed: /run/lighttpd.pid: No such file or directory
2021-06-16 13:58:37: server.c.317) unlink failed for: /run/lighttpd.pid: No such file or directory
/usr/local/etc/rc.d/lighttpd: WARNING: failed to start lighttpd
Changing the value of "var.state_dir=" to "/var/run" fix the issues.