Known issue already from my E7470 guide
Known Issue & Workaround:
HDMI-Output works but if connect HDMI-Cable the local Display goes off and never appears.
I had tried different configurations but none panned out. Here's a workaround:
Close the LID until you see the HDMI display becomes the primary display, then open the LID.
It'll switch LCD as primary and projector as secondary.