Ubuntu 20.04 on a laptop - is there any way toturn off the screen?

I had the same issue on Ubuntu 20.04 LTS server.

$ sudo vbetool dpms off

mmap /dev/zero: Operation not permitted
Failed to initialise LRMI (Linux Real-Mode Interface)

Finally I found the solution here.

You have to use 2 extra command.

In order:

sudo mount -o remount,exec /dev
sudo vbetool dpms off
sudo mount -o remount,noexec /dev

To turn on again the display:

sudo mount -o remount,exec /dev
sudo vbetool dpms on
sudo mount -o remount,noexec /dev