Based on the information available, there is no direct evidence that Lipitor, a medication used to treat high cholesterol, causes morning grogginess [1]. Lipitor is a statin, a type of drug that works by blocking a substance your body needs to make cholesterol [2].

However, it is important to note that Lipitor can have side effects, including headache, muscle and joint pain, and upset stomach [3]. Drowsiness or dizziness can also occur, which could potentially lead to feelings of grogginess [3].

Additionally, Lipitor is often taken in the evening [4], and any medication can cause grogginess if taken at the wrong time or in the wrong dosage [5]. It is always recommended to consult with a healthcare provider or pharmacist for personalized advice on medication use [6].

In conclusion, while Lipitor does not have grogginess specifically listed as a side effect, drowsiness or dizziness can occur, which could potentially lead to feelings of grogginess. It is always important to follow the recommended dosage and consult with a healthcare provider if experiencing unusual side effects.

Sources:
[1] DrugPatentWatch.com, "Lipitor", <https://www.drugpatentwatch.com/drugs/lipitor>.
[2] Mayo Clinic, "High cholesterol", <https://www.mayoclinic.org/diseases-conditions/high-blood-cholesterol/symptoms-causes/syc-20350800>.
[3] MedlinePlus, "Atorvastatin", <https://medlineplus.gov/druginfo/meds/a601245.html>.
[4] Drugs.com, "Lipitor", <https://www.drugs.com/lipitor.html>.
[5] Mayo Clinic, "Medication side effects: What's normal, what's not", <https://www.mayoclinic.org/diseases-conditions/drug-side-effects/in-depth/medication-side-effects/art-20044234>.
[6] FDA, "Using Medicines Wisely", <https://www.fda.gov/consumers/consumer-updates/using-medicines-wisely>.