Some people often unconsciously open their mouths just a bit and then close it back immediately, especially when they are working or sleeping or at the time after they wake up as shown in the below video.
Note: Sometimes it makes sound but sometimes it does not. People don't do it on purpose or they don't even know they do that.
Is it correct to say "he smacked his lips"?
In the video, it looks like he was indeed smacking his lips. And you are correct, that is what we'd call it.
The second part of your question could have a slightly different phrasing.
Some people often unconsciously open their mouths just a bit and then close it back immediately, especially when they are working...
Possible ways to describe this particular look:
His mouth went slack for a moment as he was concentrating.
His mouth hung agape as he waited in anticipation of what would happen next.
The above has less to do with the aforementioned "lip-smacking" and more to do with that look one gets when they are focused and their mouth "hangs ajar" for a brief moment.
