We used to have an old hunter who did this and we came to the conclusion he did it because he could, he enjoyed it and probably felt good. He was never stressed, or upset. I also think he did it when people came by because they would stop have a laugh and make a fuss of him.
No, that's mouthing and a totally different thing. Clapping lips is just one of those funny habits that some horses do when they are relaxed,but most don't. Many humans do something that is unique to themselves spontaneously. I had to see the careers officer when I was 16 at school and his nickname was DumptyDum Reynolds. I had no idea why until he said something or other then, finished the sentence by saying dumptydum under his breath. I nearly burst trying not to laugh. I had to endure several more DDs before I was sent on my way back to my lessons. He must have been a guitar player too because he had REALLY long (and not very clean) fingernails on his right hand, and short cut ones on his lefthand.
Tasting the air? Dogs are sometimes said to "chew the scent" and in their case it seems to be a away of getting more air in contact with the scent receptors in the nose. But the DD explanation also sounds credible!
Mine does it when he is cross with me for taking too long with his food bowl, or if everyone else goes out and he doesn't, or anything that could cause impatience, really. I think it is attention seeking behaviour.