My system consists of Ubuntu Desktop and a lot of additional server software, like Bind, Apache, Postfix.
I had the same problem: The configuration network configuration inputs from the GUI (settings > network) did not go into
/etc/resolv.conf. Also the inputs from
netplan did not got into
/etc/resolv.conf. With this solution
nslookup work correctly.
The symbolic link
/etc/resolv.conf points actually to
/run/systemd/resolve/stub-resolv.conf. After the following solution it points to
$ sudo rm /etc/resolv.conf
$ sudo ln -s /run/systemd/resolve/resolv.conf /etc/resolv.conf