lighttpd documentation
As others have noted, you need to configure DNS for domain names.
If you configure DNS with
myrouter.com 192.168.10.1
mycloud.com 192.168.10.1
then you can configure lighttpd to respond to them separately
$SERVER["socket"] == ":80" {
$HTTP["host"] == "mycloud.com" {
...
}
#else {
# ...
#}
}
$SERVER["socket"] == ":81" {
$HTTP["host"] == "myrouter.com" {
...
}
#else {
# ...
#}
}
lighttpd will still be listening on both ports, and can be configured to respond with a default site different from the other two, if desired.
If you are using TLS, then you should configure TLS certificates with those names, and tell lighttpd about those certificates.