If you see the same thing on both displays, you should start by making sure the displays are Extended instead of Mirroring ...

Using a laptop as a monitor for another computer allows you to not only mirror your computer's screen on the laptop but also extend it, meaning you can show different content on both screens.

Your laptop is now ready for closed-lid use. Go ahead and plug in your external monitor. If you want more screen real estate, you can even set up dual monitors on the Windows laptop too.