How can one turn the laptop screen off but keep the LCD screen attached to it working?

Press Win+P

In Windows 7, choose the Projector Only option.

In Windows 8 and Windows 10, choose the Second screen only option.

Go to Control Panel and then choose System and Security.

Choose Power Options and then select Choose What Closing the Lid Does from the left pane.

On When I close the lid option select "Do Nothing" for both "On Battery" and for "Plugged in".

Click Save changes

That is it, now you can close the laptop screen and keep working on your LCD.