If you see that they purse their lips, that is usually a sign that something is wrong. If you are talking to them and they do this, it might indicate that they feel very uncomfortable in your presence. But it can also mean that they don’t like the topic or the question you’re asking. Try changing the subject and take a look at their mouth again. Moreover, biting or pursing their lips is a way in which they can calm themselves if they feel anxious.