While the tvheadend docs seem to be outdated and some proxy configuration is only available for apache and nginx in latest FAQ I will share my working configuration for lighttpd here in the hope that somebody searching for it can find it.

I'm running HTS Tvheadend 4.3 from deb-multimedia on Debian 12 alias bookworm with lighttpd 1.4.69 as a reverse proxy.

Steps to enable a working setup with tvheadend and lighttpd as reverse proxy :

Enable the proxy protocol in tvheadend
Using the WebUi, make sure there is a checkmark under Tab "Configuration > General > Base" and Area "Http Server Settings"

OR
Alter the config file under <tvheadend-usr-dir>/.hts/tvheadend/config
(the <tvheadend-usr-dir> is often /home/hts .. in this case would be /home/hts/.hts/tvheadend/config)
and make sure you have 1 entry like :
```
"proxy": true,
```

Set the TVH_HTTP_ROOT if you haven't already
altered http_root in my /etc/default/tvheadend :

# https://tvheadend.org/d/3769-last-testing-builds-are-not-working-through-reverse-proxy-solved/2
TVH_HTTP_ROOT="/tvheadend"

When you alter a config file of tvheadend you need to restart tvheadend ala "sudo service tvheadend restart" or "sudo systemctl restart tvheadend.service".

I found an issue with debian's default service file for tvheadend stored in /lib/systemd/system/tvheadend.service . The problem is that it only reads the variables TVH_USER, TVH_GROUP and TVH_ARGS. I solved that by providing my own service file under /etc/systemd/system/tvheadend.service that overrules the former one via calling the init.d service (which considers all variables from /etc/default/tvheadend) via systemd as follows:

[Unit]
Description=Tvheadend - a TV streaming server and DVR
After=auditd.service network.target local-fs.target

[Service]
Type=forking
PIDFile=/run/tvheadend.pid

## using a wrapper approach, while too hard to handle optional variables from /etc/default/tvheadend
# We run tvheadend via the /etc/init.d/tvheadend script which acts as a
# wrapper picking up extra configuration files and then execs tvheadend itself
ExecStart=/etc/init.d/tvheadend start

ExecStop=/etc/init.d/tvheadend stop

ExecReload=/etc/init.d/tvheadend force-reload

Restart=on-failure
RestartSec=54s

[Install]
WantedBy=multi-user.target

Configure lighttpd to serve as a reverse proxy for tvheadend
my /etc/lighttpd/conf-enabled/10-proxy.conf :

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

server.modules  += ( "mod_proxy" )
server.modules  += ( "mod_rewrite" )

# it seems e.g. /tvheadend/redir/theme.css provides the wrong uri "/tvheadend/static/tvh.blue.css.gz",
# because the proxied HTTP_ROOT is not "/tvheadend" (like on port 9981), but "/services/tvheadend" on the reverse proxy
# tvheadend doesn't know about that, only the proxy
url.rewrite-once = ( "^/tvheadend/static/(.*)" => "/services/tvheadend/static/$1" )

$HTTP["url"] =~ "^/services/tvheadend(?:/?|/.*)" {
    proxy.header = ("map-urlpath" => ( "/services/tvheadend/" => "/tvheadend/", ),
                               "upgrade" => "enable",
    )    
    proxy.server  = ( "" => ( # proxy all file extensions / prefixes
        "tvheadend-proxy" => # optional label to identify requests in logs
            (   "host" => "127.0.0.1",
                "port" => 9981,
            ),
        )
    )
}

When you alter a config file of lighttpd you need to restart lighttpd ala "sudo service lighttpd restart" or "sudo systemctl restart lighttpd.service".

When you encounter something unexpected checking lighttpd's log files (usually below /var/log/lighttpd/ can give some indications. Look for 401 (Unauthorized) and 404 (Not Found) log entries when accessing tvheadend through lighttpd.