Based on the available information, it does not seem common for Lipitor (atorvastatin) to cause lip stiffness.

According to the Mayo Clinic, potential side effects of Lipitor include muscle pain, liver damage, and digestive problems [2]. The National Health Service (NHS) also lists muscle pain, digestive problems, and liver problems as possible side effects, along with a few others [3]. However, neither source mentions lip stiffness as a potential side effect of Lipitor.

It is important to note that, while these sources provide extensive lists of potential side effects, they may not be comprehensive. Additionally, everyone's body reacts differently to medication, so it is possible for some people to experience side effects not listed here. If you are taking Lipitor and are experiencing lip stiffness or any other unusual symptoms, it is best to consult with a healthcare professional.

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/>