I am reading a job advertisement / specification that mentions "support[ing] LAN applications" and I have no idea what it is and can't find anything on the internet. What would you normally understand this term to mean, in this context?
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.