Just to make sure things are clear:
You have a laptop with an external monitor hooked up to it running fedora workstation.
You power on the laptop
- At this point the laptop lid is open, and everything is displayed on the external monitor.
- The login screen comes up on the external monitor. You than log in and then shut the lid on the laptop. If you wait long enough for the desktop to come up it does not shut off.
If you look at /etc/systemd/logind.conf
You’ll probably want to change one or both of the top two to ignore.