Is there a way to programmatically put an AndroidWear device into "Cinema Mode"?
I would like the screen to be locked so that touches don't register on the screen.
You cannot programmatically enter theater mode on Android Wear. It has to be done by the user.
However, you can write an AlwaysOn app https://developer.android.com/training/wearables/apps/always-on.html and then control what is shown on the display. You could render a black background with some simple text, or none at all, depending on what you are trying to achieve.