Final answer:
The lesion causing left hemiplegia and right ptosis with eye deviation likely lies in the brainstem, which houses cranial nerve nuclei and motor pathways such as the corticospinal tract close together.
Step-by-step explanation:
The clinical presentation of left hemiplegia with right ptosis and an eye deviated to the right and down suggests a lesion affecting multiple neurological pathways. The right-sided ptosis and eye deviation indicate a dysfunction of the cranial nerves responsible for ocular movements, particularly the third cranial nerve (oculomotor nerve) due to its role in eyelid elevation and most eye movements. The left hemiplegia suggests involvement of the motor pathways, specifically the left corticospinal tract, as it crosses at the level of the medulla oblongata and descends to control voluntary movements on the opposite side of the body.
Considering both cranial nerve and motor pathway involvement, the lesion is likely in the brainstem, where these pathways are in close proximity. The brainstem is also where the nuclei of the cranial nerves are located. Diseases such as a stroke or brainstem tumor may result in such a presentation.