Lighttpd

Assuming you have set your port as:

server.port = 80

$HTTP["scheme"] == "http" {
   url.redirect = ("" => "https://${url.authority}${url.path}${qsa}")
}

$SERVER["socket"] == ":443" {
    ssl.engine   = "enable" 

    ssl.pemfile               = "/etc/lighttpd/ssl/cyctera.com/mydomain_com.pem" 
    ssl.ca-file               = "/etc/lighttpd/ssl/mydomain.com/intermediate.crt" 

    # curl https://ssl-config.mozilla.org/ffdhe2048.txt > /path to/dhparam
    ssl.dh-file               = "/etc/lighttpd/ssl/mydomain.com/dhparam" 

    # intermediate configuration
    ssl.openssl.ssl-conf-cmd = ("Protocol" => "ALL, -SSLv2, -SSLv3, -TLSv1, -TLSv1.1")
    ssl.cipher-list           = "ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:DHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES256-GCM-SHA384" 
    ssl.honor-cipher-order    = "disable" 

    # HTTP Strict Transport Security (63072000 seconds)
    setenv.add-response-header  = (
        "Strict-Transport-Security" => "max-age=63072000" )
}

I'd personally suggest you start off with a minimal set of settings like:

$HTTP["scheme"] == "http" {
   url.redirect = ("" => "https://${url.authority}${url.path}${qsa}")
}

$SERVER["socket"] == ":443" {
    ssl.engine   = "enable" 
    ssl.pemfile               = "/etc/lighttpd/ssl/cyctera.com/mydomain_com.pem" 
    ssl.ca-file               = "/etc/lighttpd/ssl/mydomain.com/intermediate.crt" 
    setenv.add-response-header  = ( "Strict-Transport-Security" => "max-age=63072000" )
}

Also check the error log to see if there are any errors logged if lighty fails to start (or fails to serve pages)

I have checked the error logs and they tell me nothing useful, i.e. "system exited with an error code."

Aside from the lighttpd.conf file, are there other files that need to be edited?

For example, in one set of instructions that I have found
the /etc/lighttpd/conf-available/10-ssl.conf file was was supposed to be modified like:

# /usr/share/doc/lighttpd/ssl.txt

server.modules += ( "mod_openssl" )

$SERVER["socket"] == "0.0.0.0:443" {
        ssl.engine  = "enable" 
        ssl.pemfile = "/etc/lighttpd/ssl/mydomain.com/mydomain_com.pem" 
        ssl.ca-file = "/etc/lighttpd/ssl/mydomain.com/intermediate.crt" 
        ssl.dh-file = "/etc/lighttpd/ssl/mydomain.com/dhparam.pem" 
        ssl.use-sslv2 = "disable" 
        ssl.use-sslv3 = "disable" 
        ssl.honor-cipher-order = "enable" 
        ssl.cipher-list = "EECDH+AESGCM:EDH+AESGCM:AES256+EECDH:AES256+EDH" 
}

Right, for now, it is best you include your FULL lighttpd.conf file.
Also what version of lighty are you running (see board sticky) and on what OS?

I tried the short file you recommended. I just got the usual: Job for lighttpd.service failed because the control process exited with error code. The error messages, and log files, don't tell me anything useful.

# journalctl -xe
-- Support: http://www.ubuntu.com/support
-- 
-- A start job for unit lighttpd.service has finished with a failure.
-- 
-- The job identifier is 1756 and the job result is failed.

# systemctl status lighttpd.service
● lighttpd.service - Lighttpd Daemon
     Loaded: loaded (/lib/systemd/system/lighttpd.service; enabled; vendor preset: enabled)
     Active: failed (Result: exit-code) since Mon 2020-12-28 15:01:46 MST; 11s ago
    Process: 1245 ExecStartPre=/usr/sbin/lighttpd -tt -f /etc/lighttpd/lighttpd.conf (code=exited, statu>

Dec 28 15:01:46 www systemd[1]: lighttpd.service: Control process exited, code=exited, status=255/EXCEPT>
Dec 28 15:01:46 www systemd[1]: lighttpd.service: Failed with result 'exit-code'.
Dec 28 15:01:46 www systemd[1]: Failed to start Lighttpd Daemon.
Dec 28 15:01:46 www systemd[1]: lighttpd.service: Scheduled restart job, restart counter is at 5.
Dec 28 15:01:46 www systemd[1]: Stopped Lighttpd Daemon.
Dec 28 15:01:46 www systemd[1]: lighttpd.service: Start request repeated too quickly.
Dec 28 15:01:46 www systemd[1]: lighttpd.service: Failed with result 'exit-code'.
Dec 28 15:01:46 www systemd[1]: Failed to start Lighttpd Daemon.

Post output of:
1. #/usr/sbin/lighttpd -v
2. #cat /etc/lighttpd/lighttpd.conf

PS: the snippet conf I provided was just that, a snippet!

Thank you reply. I am getting the same thing.

# lighttpd -v
lighttpd/1.4.55 (ssl) - a light and fast webserver

# cat /etc/lighttpd/lighttpd.conf

$HTTP["scheme"] == "http" {
   url.redirect = ("" => "https://${url.authority}${url.path}${qsa}")
}

$SERVER["socket"] == ":443" {
    ssl.engine   = "enable" 
    ssl.pemfile               = "/etc/lighttpd/ssl/mydomain.com/mydomain_com.pem" 
    ssl.ca-file               = "/etc/lighttpd/ssl/mydomain.com/intermediate.crt" 

    # curl https://ssl-config.mozilla.org/ffdhe2048.txt > /path to/dhparam
    ssl.dh-file               = "/etc/lighttpd/ssl/mydomain.com/dhparam.pem" 

    # intermediate configuration
    ssl.openssl.ssl-conf-cmd = ("Protocol" => "ALL, -SSLv2, -SSLv3, -TLSv1, -TLSv1.1")
    ssl.cipher-list           = "ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:DHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES256-GCM-SHA384" 
    ssl.honor-cipher-order    = "disable" 

    # HTTP Strict Transport Security (63072000 seconds)
    setenv.add-response-header  = (
        "Strict-Transport-Security" => "max-age=630c72000" )
}

# cat /etc/lighttpd/conf-available/10-ssl.conf

# /usr/share/doc/lighttpd/ssl.txt

server.modules += ( "mod_openssl" )

$SERVER["socket"] == "0.0.0.0:443" {
        ssl.engine  = "enable" 
        ssl.pemfile = "/etc/lighttpd/ssl/mydomain.com/mydomain_com.pem" 
        ssl.ca-file = "/etc/lighttpd/ssl/mydomain.com/intermediate.crt" 
        ssl.dh-file = "/etc/lighttpd/ssl/mydomain.com/dhparam.pem" 
#       ssl.use-sslv2 = "disable" 
#       ssl.use-sslv3 = "disable" 
#       ssl.honor-cipher-order = "enable" 
#       ssl.cipher-list = "EECDH+AESGCM:EDH+AESGCM:AES256+EECDH:AES256+EDH" 
        ssl.cipher-list = "HIGH" 
}

@walterbyrd

Similar to https://redmine.lighttpd.net/boards/2/topics/9558, you are posting on this site, so you should read the documentation on this site, which has the authoritative documentation for lighttpd.
lighttpd TLS docs
mod_redirect