In 1952, a person named Abdul Amir Majeed (b. 1916, d. ?) was awarded a PhD from Ohio State University with a dissertation entitled Libya: A Geopolitical Study. As far as I can find so far, it seems to be the first PhD about Libya—the main reason for posting it here, as it is a fairly superficial overview of Libyan history, geography, climate, and social structure, containing information also found in other sources of the time. It seems to have largely been written prior to the foundation of the Libyan state in 1951, and so contains quite a few comments alluding to problems to face the new state, while also providing a rather hesitant outlook on the success of the new national project. Some quotes:

"Fortunately the new state of Libya has a homogeneous population, one that
shares common ethnological origin, practises one religion and speaks a common language." (202)

"The repercussions resulting from Libyan independence will be most significant in Africa, the continent which has already been profoundly affected by this action" (221)

"Libya is the land to which the United Nations has just handed mankind’s greatest political attainment - self-government. Were this experiment being undertaken in any period but that of the cold war of 1952, it would be a most hopeful and inspiring advance over colonialism. But, actually, by the hoisting of the flag of Libyan independence, grave political and strategic questions for the western world are raised in a sensitive and important area" (223)