No, the problem is on the router. If you have assigned 192.168.1.9 to the LAMP server, then the router needs to be configured to port forward any requests it receives at port 80 on the public address on the internal address 192.168.1.9 at port 80.
As long as on the LAN you can see the site by 192.168.1.9 in the address bar, then just get the port forwarding set from the 184.108.40.206 at 80 to 192.168.1.9 at 80.
The gateway is the router's address, which you said is 192.168.1.1, and broadcast is 192.168.1.255. This is all basic networking info. A little google time or a search here would have solved this for you easily.
# The primary network interface
iface eth0 inet static