Lipitor is a brand name for atorvastatin, a medication used to lower cholesterol levels in the body. While there is some debate about the effect of statins, the class of drugs to which Lipitor belongs, on cognitive impairment, studies have shown mixed results.

A study published in the Journal of the American College of Cardiology [2] found that long-term use of statins was associated with a lower risk of dementia in older adults. However, another study published in the Journal of the American Medical Association [3] found that statin use was associated with a higher risk of cognitive impairment.

The Health Harvard Medical School [1] suggests that the risk of cognitive impairment may be increased in people who are already at risk for dementia, such as those with a family history of the disease. However, the risk is relatively small and the benefits of taking statins to lower cholesterol levels may outweigh the potential risks.

Overall, while there is some evidence to suggest that statins may affect cognitive function, more research is needed to fully understand the relationship between statins and cognitive impairment.

Sources:
[1] https://www.health.harvard.edu/staying-healthy/do-statins-increase-the-risk-of-dementia
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5830056/
[3] https://www.drugpatentwatch.com/p/tradename/LIPITOR