**Core Concept**
The cellular adaptations in this patient will be influenced by her unique combination of being a lactating mother and having a history of hepatectomy. This scenario involves the interplay of several physiological and pathological processes, including the body's response to liver damage, the demands of lactation, and the body's compensatory mechanisms to maintain homeostasis.

**Why the Correct Answer is Right**
In a lactating mother, the liver is actively involved in the production and secretion of very-low-density lipoproteins (VLDLs) to supply fatty acids to the mammary glands for milk production. This process requires an increase in the synthesis and secretion of VLDLs, which is achieved through an increase in the expression and activity of enzymes involved in lipid synthesis, such as fatty acid synthase and acetyl-CoA carboxylase. Additionally, the liver's ability to detoxify and metabolize drugs is compromised after a hepatectomy, leading to an increase in the expression of cytochrome P450 enzymes to compensate for the reduced liver mass.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the liver's response to hepatectomy would not primarily involve the increase in glycogen synthesis, which is more relevant to the body's response to starvation or increased energy demands.
* **Option B:** This option is incorrect because the liver's involvement in lactation would not primarily involve the increase in protein synthesis, which is more relevant to the body's response to muscle injury or inflammation.
* **Option C:** This option is incorrect because the liver's response to hepatectomy would not primarily involve the decrease in lipid synthesis, which is actually increased to support lactation.

**Clinical Pearl / High-Yield Fact**
In a lactating mother with a history of hepatectomy, the liver's ability to detoxify and metabolize drugs is compromised, and the expression of cytochrome P450 enzymes is increased to compensate for the reduced liver mass. This can lead to altered pharmacokinetics and increased sensitivity to certain medications.

**Correct Answer: C. Increased lipid synthesis.**