local LAN access mode for devices running plex app?

@networkspeedy said:
The devices then connect to my media server via a connection going out over the internet.

No, they don’t. They ask plex.tv for the IP adresses of your server. plex.tv answers with a list of IP adresses. This list contains both the public and the private (local) IP adress of your server. If the plex client in question can reach your server on its private adress, it will connect directly.

This is the normal operation and it works in 95% of cases.

There is a situation, where this strategy will fail:

  1. When you ‘require’ SSL on the server (Settings - Server - Network - Secure connection) and
  2. your router supresses DNS rebinding

When these 2 conditions meet, a local, direct connection won’t be possible, because the certificate won’t match.
Either set secure connections to ‘preferred’ or tell your router to allow DNS rebinding for the domain plex.direct
More information on this specific topic

This is also the reason why you should never, ever use an own local domain name for your server.
Always use either the local (private) IP or go to plex.tv and press ‘Launch’
https://support.plex.tv/hc/en-us/articles/200288666-Opening-Plex-Web-App