If a laptop is monitored (say from employer) and I boot it from an external USB hard drive or a LIVE-CD/USB-Stick, can it then still be monitored somehow?
While it is technically possible to do so, it would require modifying the device firmware to spy on the running operating system. The chances that your employer would do this are astronomically low.
It is feasible that some laptop manufacturer could design (or has already designed) firmware with a feature to log information about each booted machine, in which case you would need to disable that feature. I suggest you check your BIOS/UEFI to make sure you see nothing like that.
As forest mentioned it is possible the firmware was modified to log your activities, however another aspect to be aware of is if you're using your employers internet.
If you boot your laptop from an external source but then connect to your work internet, your employer could still potentially see the traffic to/from your device. Using your own internet source, or a service like a VPN can counteract this.