**Core Concept**
The question is testing the understanding of embryonic development, specifically the formation of the face and palate. The cleft lip and palate are congenital anomalies resulting from the failure of fusion of facial and palatal processes during embryonic development.

**Why the Correct Answer is Right**
The development of the face and palate involves the fusion of several facial processes, including the frontonasal process, maxillary processes, and medial nasal processes. The fusion of these processes occurs around the 6th to 8th weeks of gestation. A failure of fusion between the medial nasal process and the maxillary process results in a cleft lip and palate. This is most commonly due to a failure of the medial nasal process to contribute to the formation of the upper lip and primary palate. This process is crucial for the development of the philtrum of the lip, the primary palate, and the alveolar ridges.

**Why Each Wrong Option is Incorrect**
**Option A:** Failure of the frontonasal process to contribute to the formation of the upper lip and primary palate would result in a different set of anomalies, such as a midline cleft lip and palate or a proboscis-like nose.
**Option B:** Failure of the maxillary process to contribute to the formation of the upper lip and primary palate would result in a unilateral cleft of the primary palate, but not the cleft lip.
**Option C:** Failure of the lateral nasal process to contribute to the formation of the ala of the nose would result in a different set of anomalies, such as a cleft ala of the nose.

**Clinical Pearl / High-Yield Fact**
The embryonic development of the face and palate is a complex process involving the fusion of several facial processes. A failure of fusion between the medial nasal process and the maxillary process is a common cause of cleft lip and palate.

**Correct Answer:** C.