I'm not sure what the real problem is here. If the gateway computer and the computer upon which your Perl program runs (the client computer) are configured properly, the networking internals should direct your signal to the internet computer if you give it that computer's address. Your program shouldn't even have to know the LAN address of the gateway computer to do what you want. This assumes two things:

1. The gateway computer is properly configured for network address translation.

2. The client computer's networking is set up to route all requests to the "outside" through the gateway computer.

Given this, there should be nothing your program needs to know about how its request gets to the internet, nor how the reply gets back. That's the magic of network routing.