Based on the available information from Mayo Clinic and the NHS, lip stiffness is not explicitly listed as a common side effect of Lipitor, which is the brand name for the drug atorvastatin [2][3]. Lipitor is a medication used to treat high cholesterol levels [1].

The Mayo Clinic provides a list of possible side effects of Lipitor, including muscle pain, liver problems, and digestive issues, but does not mention lip stiffness [2]. Similarly, the NHS lists potential side effects such as headaches, feeling sick, muscle pain, and dizziness, but does not include lip stiffness [3].

It is important to note that everyone's reaction to medication can vary, and some people may experience side effects not listed in the common side effects. If you are taking Lipitor and have concerns about any new symptoms, it is recommended that you consult with your healthcare provider [2][3].

In summary, based on the available information from Mayo Clinic and the NHS, lip stiffness is not a commonly reported side effect of Lipitor.

Sources:
[1] <https://www.drugpatentwatch.com/p/tradename/LIPITOR>
[2] <https://www.mayoclinic.org/drugs-supplements/atorvastatin-oral-route/side-effects/drg-20067003>
[3] <https://www.nhs.uk/medicines/atorvastatin/side-effects-of-atorvastatin/>