|external can be your own hosted web server or a server on the internet or a server in someone elses lan via the internet. |
Hence the request for clarification.
Your "external" ip would be that of YOUR router or that of the service you pay for if you are having someone else provide that router service.
It is normal to have your router or the one being provided NOT to return icmp [ping] packets. Though usually you can't ping it from the lan side either if it is configured to drop icmp packets.