Lipitor is a medication that is used to lower cholesterol levels in the body. It works by blocking the production of cholesterol in the liver. According to the drug patent watch [1], Lipitor's active ingredient is Atorvastatin Calcium.

The effectiveness of Lipitor is not necessarily dependent on a low-fat diet. However, a healthy diet and lifestyle changes are often recommended in conjunction with the medication to improve its effectiveness. As stated by WebMD [2], Lipitor is usually prescribed along with a low-fat diet and exercise program to help lower cholesterol levels.

A study published in the National Center for Biotechnology Information [3] found that a low-fat diet can help improve the effectiveness of statins, such as Lipitor. The study found that a low-fat diet can help lower LDL cholesterol levels, which is the "bad" cholesterol that Lipitor targets. However, the study also found that the effectiveness of statins is not solely dependent on a low-fat diet and that medication is still necessary to achieve optimal cholesterol levels.

In conclusion, Lipitor is effective in lowering cholesterol levels regardless of the diet. However, a low-fat diet and lifestyle changes are often recommended in conjunction with the medication to improve its effectiveness. A study found that a low-fat diet can help improve the effectiveness of statins, such as Lipitor, but medication is still necessary to achieve optimal cholesterol levels.

Sources:
[1] https://www.drugpatentwatch.com/p/tradename/LIPITOR
[2] https://www.webmd.com/drugs/2/drug-3330/lipitor-oral/details
[3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1312230/