I have been using Moodle on LAN, for various features of moodle, Thanks to MOODLE community.
We have installed Moodle using WAMP and XAMPP, 2 instances.
The webserver DNS are the DNS of the Doamin sever from where we distribute the internet.
EX. 192.168.0.1--Domain sever
DNS -- 192.168.0.1 and 22.214.171.124, this DNS is on each PC.
So it works fine without internet, yes we have theme installed for which it requires internet, as it links to the google fonts.
I think this will help you...