Final answer:
The lesion causing a left-arm hemiballismus would most likely localize to the right subthalamic nucleus, as the basal ganglia and motor control in the brain are cross-wired.
Step-by-step explanation:
The lesion causing a left-arm hemiballismus would most likely localize to the right subthalamic nucleus. Hemiballismus is characterized by involuntary flinging movements of the limbs and is often the result of damage to the subthalamic nucleus of the basal ganglia, particularly on the contralateral side of the affected limbs. Since the brain and body are cross-wired (the left side of the brain controls the right side of the body and vice versa), a lesion in the right subthalamic nucleus would likely cause left-arm hemiballismus.