**Core Concept**
The patient's symptoms, recurrent swelling of the lips without itching, suggest an allergic reaction, specifically an immune complex-mediated process. This condition is often associated with a genetic predisposition, involving an abnormal immune response to environmental allergens.

**Why the Correct Answer is Right**
The patient's symptoms are characteristic of angioedema, which is often linked to a deficiency of C1 esterase inhibitor (C1-INH). C1-INH is a crucial protein that regulates the activation of the classical complement pathway and the contact activation system. In its absence, the immune complex-mediated response becomes uncontrolled, leading to the release of histamine and other mediators, causing angioedema. The genetic deficiency is inherited in an autosomal dominant pattern, explaining the family history.

**Why Each Wrong Option is Incorrect**
**Option A:** Serum complement levels are often normal in patients with C1-INH deficiency, so this is not a reliable marker for the condition.
**Option B:** While histamine is involved in the pathogenesis of angioedema, its deficiency is not the primary cause of this patient's symptoms.
**Option C:** There is no strong association between C3 deficiency and angioedema.

**Clinical Pearl / High-Yield Fact**
C1-INH deficiency is a rare genetic disorder that can be inherited in an autosomal dominant or recessive pattern. It is essential to consider this diagnosis in patients with recurrent angioedema, particularly those with a family history of the condition.

**Correct Answer:** C. C1 esterase inhibitor.