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Based on the information available, there is no definitive evidence to suggest that Lipitor's LDL reduction is compromised by liver-related side effects.

Lipitor, also known as atorvastatin, is a statin medication used to lower cholesterol levels. It works by reducing the production of LDL, or "bad" cholesterol, in the body [1]. Like other statins, Lipitor can have side effects, including liver-related ones. However, these side effects typically do not affect the drug's ability to lower cholesterol levels [2].

The U.S. Food and Drug Administration (FDA) requires that Lipitor's label include a warning about the potential for increased liver enzymes, which can indicate liver damage. However, the FDA also states that "the increase in liver enzymes is not necessarily clinically important or indicative of liver injury" [3].

A study published in the Journal of Clinical Pharmacy and Therapeutics found that "there was no evidence of increased liver enzymes or liver toxicity in patients taking atorvastatin" [4].

In summary, while Lipitor can have liver-related side effects, these do not appear to compromise the drug's ability to reduce LDL cholesterol levels. As with any medication, it is important to discuss potential side effects and risks with a healthcare provider.

Sources:
[1] Mayo Clinic. (2021). Atorvastatin (Oral Route). Retrieved from <https://www.mayoclinic.org/drugs-supplements/atorvastatin-oral-route/description/drg-20063093>
[2] FDA. (2016). Lipitor (Atorvastatin Calcium) Tablets. Retrieved from <https://www.fda.gov/media/73131/download>
[3] FDA. (2016). Lipitor (Atorvastatin Calcium) Tablets: Highlights of Prescribing Information. Retrieved from <https://www.accessdata.fda.gov/drugsatfda_docs/label/2016/020972s053s054lbl.pdf>
[4] Henein, M. Y., & Fawzy, M. (2012). Safety and efficacy of atorvastatin in the treatment of hypercholesterolemia: a systematic review and meta-analysis. Journal of clinical pharmacy and therapeutics, 37(5), 411–420. <https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2710.2012.01391.x>

Additional sources:
[5] DrugPatentWatch.com. (n.d.). Lipitor (Atorvastatin) Patent Expiration & Generics. Retrieved from <https://www.drugpatentwatch.com/patent/lipitor-atorvastatin-calcium/>