This is basically a DNS issue.
As long as you configure Plesk to use internal IPs on your LAN, all that's needed is a mechanism to make machines on that LAN connect to the plesk server when the appropriate domain name is entered in their browser.
You can do this by manually editing the hosts file on each machine connected to the LAN (e.g. to make yourwebsite.local or subdomain.companyname.tld point to 192.168.x.x or whatver).
You can also do it all automatically by configuring each machine on the LAN to use the plesk server as a dns server and configuring the dns server on plesk to do recursive lookups for IOs on your LAN.
Or if you have some sort of server on the network already that does DNS/DHCP/whatever, you just add the appropriate records to that.