So apparently, Firefox and lighttpd 1.4.45 (current version on Debian 9/stable) dont get along very well.
You will have connexion issue, and a message "Secure Connection Failed".
It would seem that Firefox and Lighttpd/Openssl are negociating a TLS 1.3 connexion (a new RFC), which fails to establish.
A workaround/solution is to disable TLS 1.3 in lighttpd ssl.openssl.ssl-conf-cmd = ("Protocol" => "-ALL, TLSv1.2"
but that option requires lighttpd 1.4.48.
You can get it and compile it from source (currently you get 1.4.53). Follow the guide https://redmine.lighttpd.net/projects/lighttpd/wiki/InstallFromSource It goes smoothly on debian.
apt-get build-dep lighttpd
./configure --with-openssl --prefix=/usr/local
make
make install
You can also try it, without installing it thusly (from the src folder of the cloned git) :
./lighttpd -f /etc/lighttpd/lighttpd.conf -m /tmp/lighttpd1.4/src/.libs/
Here is a backport for Debian 9/stable https://github.com/AnnoyingTechnology/lighttpd-backport-debian-9-stretch