* 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

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

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.


* 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://redmine.lighttpd.net/projects/lighttpd/wiki/InstallFromSource