Tethered Via Lightroom photo orientation?

I would like the client see the images via a 23" monitor using a  Laptop running Lightroom 4 as I'm shooting.

I have yet to purchase the monitor. The issue I have is when shooting in portrait orientation they appear in landscape orientation in the loupe viewer in Lightroom, I have to manually adjust them to portrait.

If I purchase a monitor & have it in portrait orientation, will the images show correctly?

Cheers