Anxiety is the body's natural response to potential threat. The sensations you experience all reflect sudden changes the body goes through when the hormone Adrenaline is released into the bloodstream.
The physical changes that occur prepare you for intense physical action (for responding to the potential threat). This makes a lot of sense if we are talking about a physical threat, say for example, a dangerous animal. When we realize we are being threatened Adrenaline is released in the bloodstream and our body changes and gets ready for action - this is what we experience as anxiety. It's a little less obvious when the threat is not physical in nature but perhaps instead social, emotional or occupational. We are threatened by non-physical things in our lives as well, for example the possibility of being caught lying. We anticipate that we are being threatened with something we don't want and our body responds with anxiety. In a similar manner, if we are being lied to we face the threat that the person don't like us, is trying to trick us or perhaps is going to reject us.
So, the anxiety experience in relation to lying is your body reacting to the potentially threatening elements of the interaction.
People vary in the ease with which they lie. Some people probably aren't concerned about getting caught or don't care if they are and so they probably have less of the unpleasant anxiety response. Those people who are concerned about getting caught, do care if they are caught or believe they are doing something very wrong probably have a much more intense anxiety response.
I I hope this has been of some help. If you have further questions or would like me to elaborate on any part of my question please don't hesitate to let me know. Best of luck!