Lipitor (atorvastatin) is a medication that is used to lower cholesterol levels in the blood. According to Drugs.com [2], it is generally safe to consume citrus fruits while taking Lipitor, including limes and lime juice. The interaction between atorvastatin and citrus fruits is not significant enough to cause any adverse effects. However, it is important to note that grapefruit and grapefruit juice should be avoided while taking Lipitor. Grapefruit can interfere with the way that Lipitor is metabolized in the body, which can increase the risk of side effects.

In a study published in the Journal of Clinical Lipidology [3], it was found that the consumption of grapefruit juice increased the level of atorvastatin in the blood by 83%. This increase can lead to an increased risk of side effects, such as muscle pain and liver damage. Therefore, it is recommended that patients taking Lipitor avoid grapefruit and grapefruit juice.

In conclusion, while Lipitor does not interact with citrus fruits such as limes and lime juice, grapefruit and grapefruit juice should be avoided. Patients taking Lipitor should always consult with their healthcare provider before making any changes to their diet or medication regimen.

Sources:
[2] https://www.drugs.com/medical-answers/you-limes-lime-juice-taking-statin-drugs-3211550/
[3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3589309/