Hmm. The free version of NoMachine does not limit access to LAN only, I just want to make that clear.
So it must be something else. I suggest you try the following:
1) Uninstall (removing all traces completely) and reinstall. Your screenshot shows no !M icon (which is an indication of the server running) plus your screenshot actually says ‘no server running’. If the server was running, it would show the External IP.
2) If you continue to not see the External IP, from a terminal on the server please run:
sudo /usr/NX/bin/nxserver --upnpmap
sudo /usr/NX/bin/nxserver --upnpstatus
It should show something like this:
sudo /usr/NX/bin/nxserver --upnpstatus
Local IP 10.0.1.XX
Gateway IP 10.0.1.1
External IP XX.XXX.XXX.XXX
NX port 4000 mapped to: XX.XXX.XXX.XXX:23484
3) See the following article: https://www.nomachine.com/AR11L00827
If your home router doesn’t accept UPnP or NAT-PMP commands, it will be necessary to configure it through the router’s admin interface