how to disable unencrypted traffic(port 80) on lighttpd

you have to set server.port = 443 in lighttpd.conf and comment the conditional $SERVER["socket"] == "0.0.0.0:443" { } in 10-ssl.conf

keep ssl.engine = "enable" and ssl.pemfile = "/etc/lighttpd/server.pem" in 10-ssl.conf

How about, commenting out

# /etc/rc.d/lighttpd start

Or, you could comment out the fastcgi.server lines in

/etc/lighttpd/lighttpd.conf  

Ok, this is the reference I was looking for, are you using these things?

I think the bottom line is, if you just make the server.port 443 and
remove the port 80 config entirely instead of a redirect, the server would respond only on 443.