Disable 'Invisibility on LAN' - NordVPN Linux
Registered here just to answer this question. Long time lurker.
I had the same problem. There is no flag/option for the "invisibility on LAN" feature, however, you can whitelist your entire subnet or a range of it and it effectively fixes the issue.
In my case, I implemented:
nordvpn whitelist add subnet 192.168.1.0/24
This immediately opened up my LAN with NordVPN enabled.