This is a question that has attracted far more attention than most, because during the 1970s then-new-leader Muamar Gaddafi was looking for different ways to push the development of Libya, and one of the ways he did it was by supporting a massive UNESCO project to survey Roman era agricultural remains in the pre-desert region. I'm actually not certain whether this ended up having any really effect, but I always thought it was one of the neater bits of the history of archaeology. Anyway.

Anyway, one of the results of these and later surveys is to show that, in stark contrast to earlier notions, the Libyan Valley agriculture was not dependent on a drastically different climatic regime, the climate has not changed a great deal since then, nor was it responsible for desertification, in fact the water practices have been noted for their sustainability. Instead, it needs to be seen in social, economic, and above all historical terms, and that the agriculture of Roman North Africa was created by human decisions. During the Roman era North Africa became a very important agricultural breadbasket for the empire but particularly for Italy--Egypt is often talked about as a source for grain for the city of Rome but North Africa was at least as important. This meant that as these commercial relations developed, local elites had an incentive to transition from low density pastoralism and subsistence agricultural practices to high intensity systems of mass agriculture. To do this they drew on very sophisticated native practices of water management, but the result was specific to the Roman period. With he collapse of these trade routes, the incentive (and perhaps the capacity of elites to control local populations) evaporated, and returned to the agricultural regime that characterized the pre-Roman period.

A good source for this is Graeme Barker, "A tale of two deserts: contrasting desertifcation histories on Rome’s desert frontiers" which compares the locally driven process in the Libyan valleys to the more top down (and environmentally destructive) processes in contemporary Jordan.