What you are trying to accomplish is something called "clamshell mode" - lid closed operation to a TV or monitor.
Check this link
Basically you hook up your external monitor to your MBP with a USB mouse and/or keyboard attached, close the lid, then use the mouse to wake up the monitor.
With your external drive attached to the MBP, you should now be able to use the external monitor as you would normally use the MBP's monitor.
I
think I'm understanding what you need to accomplish. If I don't have it right, let me know and we'll dig deeper.
Good luck!