I have no idea what it is and can't find anything on the internet!
Expanding on ahmed's answer above...
The actual terminology used is probably ment to indicate a software application (possibly a database) running on their local LAN, possibly off the shelf, possibly bespoke. Probably running/hosted on a server with client software used to connect to it from across the local LAN.
It is an application that runs only on a LAN (Local Area Network) without internet access. The LAN could be small, 3 - 4 clients; or large with over 500 clients in multiple buildings.
Video Conferencing, Remote Access Control, Gaming Servers, all started as LAN applications.
For more information you can refer this.
Hope this helps.