Opening the lid turns on the built-in screen again. On most (all?) of the laptops I’ve seen it forces them to turn off the built-in screen, but the with above mentioned setting they remain running and display to external monitor. Turn off suspend when notebook lid is closed feature and close your notebook’s lid. There are a couple more things you can try, if you don’t have such a key. On some notebooks you have to press +, for example on a Dell I have access to at work it’s +, on an HP it looks like +. It usually is on some of - keys and usually has a screen label/icon on it (sometimes clear and sometime quite symbolic).
I’ve seen such a key on all the notebooks I’ve had in my hands (which is not that many, but more then ten). It basically made exactly for the purpose you want to use it for. I’ve just tested it (on a Gnome DE), this hotkey cycles through display configurations with a beautiful screen overlay: Mirror – Join Displays – External only – Internal only. This gets my vote! for the purpose you describe that’s the best solution. That might be more what you’re looking for. On the other hand, there’s usually a function key that turns the screen off.