Lipitor is a prescription medication used to lower cholesterol levels in the blood [1]. According to the Mayo Clinic, herbal supplements, including blood thinners, can interact with prescription medications and cause harmful side effects [2]. The American Heart Association advises that it is essential to consult a healthcare provider before taking any non-prescription medication or supplement, including blood thinners, while taking Lipitor [3]. Therefore, it is crucial to speak with a healthcare provider to determine if there are any potential interactions between Lipitor and non-prescription blood thinners before taking them together.

Sources:
[1] https://www.drugpatentwatch.com/p/tradename/LIPITOR
[2] https://www.mayoclinic.org/healthy-lifestyle/consumer-health/in-depth/herbal-supplements/art-20046488
[3] https://www.heart.org/en/health-topics/consumer-healthcare/medication-information/medication-interactions-food-supplements-and-other-drugs