Yes, iptables would work great for this. You need a rule that will drop all packets destined for a network other than that of your internal LAN.
Try this:
Assuming your internal network is 192.168.1.0/24
Code:
iptables -I OUTPUT 1 ! -d 192.168.1.0/24 -j DROP
This will drop any packet leaving the server that is not destined for an IP address located on your LAN. Since you are already behind a router you won't need to worry about incoming traffic.
I hope this helps!