Parted lips while staring, what could that mean?

I have a tendency to overlook things but when it comes to body language what does this indicate? I was starting a conversation with a guy that I'm dating and while I'm talking he just stares at me without saying a single word. He looked like he was numb or "gone" it made me uncomfortable I almost couldn't look at him because he was looking right in my eyes with lips really parted. I can't look him in the eyes mostly because whenever we do look each other in the eyes he look so deep.
Parted lips while staring, what could that mean?
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