* lighttpd responds to the following signals:

SIGTERM - shut down immediately (terminate existing connections, then exit)
SIGINT  - shut down gracefully  (serve existing connections, then exit)
SIGUSR1 - reload gracefully     (serve existing connections, then reload config)
SIGHUP  - re-open log files     (NOTE: does not reload lighttpd configuration)

(Note: SIGUSR1 behavior is available in lighttpd 1.4.46 and later)


* lighttpd graceful restart

With lighttpd 1.4.46 and later, SIGUSR1 is the recommended method to gracefully
handle configuration reloads and log rotation, though a graceful stop and then
restart of lighttpd is still required for lighttpd configurations which chroot,
or which have TLS certificates readable by root, but not by the lighttpd user.

https://blog.lighttpd.net/articles/2005/09/02/graceful-restart/
The historical way to reload lighttpd config is to gracefully stop and then to
restart lighttpd.


* lighttpd initscripts

Depending on the operating system and distribution brand, there are many
ways to set up lighttpd to run as a daemon when the system starts up, and
to send signals to lighttpd for start/stop/restart/etc.

Rather than attempting to maintain scripts for an unknown number of distros,
here are links to a few, which can be used as examples.

Arch:
https://github.com/archlinux/svntogit-packages/tree/packages/lighttpd/trunk

Debian:
https://salsa.debian.org/debian/lighttpd

Fedora:
https://src.fedoraproject.org/rpms/lighttpd/tree/rawhide

Gentoo:
https://gitweb.gentoo.org/repo/gentoo.git/tree/www-servers/lighttpd/files

openSUSE:
https://build.opensuse.org/package/show/server:http/lighttpd

sample systemd unit script: doc/systemd/lighttpd.service

Additional, updated information may be found at
https://wiki.lighttpd.net/InstallFromSource