I think you might need to install another Nagios server in that particular LAN and set up a distributed server.
The function of a distributed server is to actively perform checks all the services you define for a "cluster" of hosts. I use the term "cluster" loosely - it basically just mean an arbitrary group of hosts on your network. Depending on your network layout, you may have several cluters at one physical location, or each cluster may be separated by a WAN, its own firewall, etc. The important thing to remember to that for each cluster of hosts (however you define that), there is one distributed server that runs Nagios and monitors the services on the hosts in the cluster. A distributed server is usually a bare-bones installation of Nagios. It doesn't have to have the web interface installed, send out notifications, run event handler scripts, or do anything other than execute service checks if you don't want it to.