Once upon a time, notifications among LAN systems were handled by rwall. That system worked as intended and at least one Linux desktop environment, KDE, supported an rwall wrapper through a popup dialog.
While still functional, the rwall mechanism no longer seems supported among most distros and most desktop environments do not support popup wrappers.
Generally, the now accepted method for notification popups is
notify-send. Works great on local systems but not great across a LAN. To use
notify-send across a LAN requires ssh, which for the tech savvy is doable. For non technical users this option is clunky at best. When using ssh, a password or key pairs are needed, but a destination user account is needed either way. Key pairs are the only palatable method for scripting and automation. Knowing the appropriate $DISPLAY environment variable is needed too.
With Linux based systems there really is no nice or easy way to provide GUI desktop notifications across a LAN.
Almost 30 years ago this was a simple point-and-click exercise in Windows for Workgroups. For script writers, a simple
net send $HOSTNAME "Message" command was sufficient to provide remote GUI notifications. That command remains usable to send notifications to Linux systems, but unless using a desktop environment such as KDE, a terminal or console must be open to view the message.
My guess is the current libnotify structure could support GUI popups within desktops but lacks the appropriate hooks to function like KDE intercepting rwall messages. Developers are aware of the problem.
The year of the Linux Desktop awaits.