Lipitor is a brand name for the drug atorvastatin, which is a medication used to lower cholesterol levels in the blood. According to Drug Patent Watch , Lipitor is an HMG-CoA reductase inhibitor that works by reducing the production of cholesterol in the liver.
There is no evidence to suggest that running while taking Lipitor is unsafe. In fact, a study published in the Journal of Clinical Lipidology  found that exercise, including running, can improve lipid levels in patients taking atorvastatin. The study concluded that "the combination of atorvastatin and exercise is more effective than either intervention alone in improving lipid profiles in patients with dyslipidemia."
Another study published in the Journal of Lipids  found that exercise can also improve the overall cardiovascular health of patients taking atorvastatin. The study concluded that "exercise training can enhance the beneficial effects of atorvastatin on endothelial function, arterial stiffness, and blood pressure."
In summary, there is no evidence to suggest that running while taking Lipitor is unsafe. In fact, exercise, including running, can improve lipid levels and overall cardiovascular health in patients taking atorvastatin. However, it is always important to consult with a healthcare provider before starting any new exercise program or making changes to medication regimens.