The correct answer is D. Inferior alveolar nerve.
The inferior alveolar nerve, and its branch the mental nerve, provide sensory innervation of the lower lip. As such, it is necessary to anesthetize that nerve most crucially in order to remove the lesion.
The auriculotemporal nerve provides sensation to the temporomandibular joint, the buccal nerve provides sensation to the buccal mucosa, the greater auricular nerve provides sensation to the angle of the jaw, and the lingual nerve provides sensation to the anterior tongue and lower gingivae. Although the lingual nerve may be a necessary one to control sensation during dissection, the lower lip is innervated separately.
References:
Flowers FP, Goldsmith CB, and Steadmon M. Surgical Anatomy of the Head and Neck in: Bolognia J. L., Jorizzo J. L., Rapini R. P., et al. Dermatology, 2003, Elsevier.
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