Hello Elliot, since there s no large blood vessel in the lips, there s no way that the pulse vibration could be transmitted to them. Involuntary movement of the lips (or other parts of the body) is probably due to muscle activation. This can be caused (sometimes) by psychological tension in susceptible individuals. It could also be caused by muscle fatigue - overuse of a group of muscles. Hypertension has nothing to do with it. If it won t go away by itself, you should consult a neurologist for further investigation. Neurologic conditions may also present with tics. I hope I ve helped! If you d like more clarifications, please let me know. I ll be glad to provide them. Kind Regards!