1) Unattended-upgrade at shutdown and after Lightdm is stopped: Perhaps
a solution would be to :
- stop and disable the unattended-upgrade systemd service
- edit the unattended-upgrades config file to setup the shutdown to false
- write/enable/start your custom systemd service that runs
/usr/bin/unattented-upgrade only after shutdown has been asked and the
lightdm systemd service has been stopped
2) unattended-upgrades notifications while Plymouth is running: I do not
read Python but trying to understand this python script, I have the
impression that Plymouth does notify the user that unattended-upgrédes
is running
Good luck ;-)