All new releases of the LG Plex app would appear here, and you would not really need to take any action to get it normally due to how the app loads.
I have no idea how one would obtain a beta app unless there is some private unlisted app loader you can obtain on the LG Content Store by invitation or sideload.
Honestly the best suggestion I have (which you probably don’t want) is to get an Android/Fire OS device for your client instead of using the LG one, because those you have the ability to side load an older version of the Plex client and avoid bad releases (plus they support more audio and subtitle formats).
