Based on the information available, there can be potential interactions when combining Lipitor (atorvastatin), a cholesterol-lowering medication, with grapefruit oil.

Grapefruit oil, like the fruit itself, can interact with various medications, including Lipitor. This is because certain compounds in grapefruit can inhibit an enzyme in the intestines that is responsible for breaking down drugs, leading to increased levels of the medication in the bloodstream [1].

According to DrugPatentWatch.com, "Grapefruit juice can increase the amount of atorvastatin in your body, which can increase your risk of serious side effects" [2]. These side effects can include liver damage, muscle damage, and kidney problems.

However, it is important to note that this interaction is not typically associated with grapefruit oil to the same extent as with the consumption of the actual fruit or juice. This is because the oil contains different compounds and in different concentrations than the fruit or juice [3].

Despite this, it is still recommended to exercise caution and consult with a healthcare provider before combining Lipitor with grapefruit oil, or any other medication, to avoid potential interactions and side effects [1][2].

Sources:
[1] Mayo Clinic. (2021). Grapefruit Juice and Some Drugs: A Dangerous Mix. <https://www.mayoclinic.org/healthy-lifestyle/nutrition-and-healthy-eating/in-depth/grapefruit-juice/art-20047848>.
[2] DrugPatentWatch.com. (n.d.). Atorvastatin (Lipitor) Drug Interactions. <https://www.drugpatentwatch.com/drugs/atorvastatin/interactions>.
[3] National Center for Complementary and Integrative Health. (2016). Grapefruit and Some Drugs Don't Mix. <https://www.nccih.nih.gov/health/grapefruit-and-some-drugs-dont-mix>.