Incorrect. The femoral nerve carries somatic sensory and motor to the anterior thigh.

Incorrect. The greater splanchnic nerve carries visceral sensory and motor to the foregut.

Correct! The lesser splanchnic nerve carries visceral sensory and motor control to the midgut. As the cecum is a midgut organ sensory information could return via the lesser splanchnic nerve.

Incorrect. The least splanchnic nerve carries visceral sensory and motor to the hindgut (via the hypogastric plexus). 

Correct! The vagus carries visceral sensory and motor information to thoracic organs (e.g. lungs, heart, esophagus, etc.) and to the foregut/midgut (but not the hindgut). As the cecum is a midgut structure, sensory information could return via the lesser splanchnic nerve.  

Incorrect. The lumbar ventral primary rami carries somatic sensory and motor to the body wall and lower extremities, not to organs themselves.

Possible, but less likely. The iliolumbar nerve carries somatic sensory and motor to the body wall. While this nerve innervates the body wall close to the cecum, the lesion would have to be causing body wall irritation for sensation to pass back along the iliolumbar nerve.

Incorrect. The Ilioinguinal nerve carries somatic sensory and motor to the region of the inguinal canal, somewhat distant from where the cecum is located.