From an earlier answer of mine

There were some isolated discoveries during the 1920s that hinted at the possibility of oil deposits in the colony. Wells sometimes produced commercially-negligible amounts of petroleum and natural gas. An Italian geological expedition led by the explorer and geologist Ardito Desio did discover oil in the late 1930s. Despite these discoveries, there was next to no exploitation of Libya's petroleum deposits while Italy controlled the region. This was not due to lack of foresight on the part of the Italians, but a constellation of interlocking factors that prevented the region's reserves from being exploited until over a decade into the postwar era.

One of the factors inhibiting oil exploration was political. The Italian occupation of Libya prioritized its development as a settler colony for modern agriculture. This meant there was greater pressure to find and exploit aquifers rather than drill for oil. Italian colonization also prompted a fierce Libyan resistance movement and pacification campaign that reached a peak during the 1920s. The violence in the region put a damper on major geological expeditions into the interior until the 1930s. While the Italian colonial government was receptive to exploring the region for oil in the 1920s, this was not its main priority. Any thought of petroleum deposits in this period were largely hypothetical and not worth devoting scarce resources towards their exploitation.

The lateness of the geological expeditions points to another factor limiting the Italians: knowledge. The Italians only made progress on making detailed geological surveys of the interior of the country after the pacification of the Libyan population. This meant that it was only in the mid-1930s that geographers had some inkling of which regions would possibly have petroleum deposits in them. Adding to these problems, petroleum deposits in Libya require deep drilling. The state-owned oil company, AGIP, had far less experience in exploration and deep-drilling than more-established rivals like Shell or Standard Oil. Moreover, most of AGIP's activities in the Italian sphere of influence were focused more on Albania than Libya.

Nonetheless, Desio was able to persuade the AGIP to conduct a two-year reconnaissance campaign in the Libyan desert after his discovery of oil in 1938. Desio correctly predicted that the Sirte basin was he ideal spot for finding petroleum. Yet, AGIP's campaign failed for a number of reasons. Inexperience with deep drilling and exploration meant that the reconnaissance campaign was slow-moving. Harsh desert conditions also ensured that AGIP's machinery frequently broke down. The outbreak of the war further curtailed operations and this exploratory expedition was cut short.

Knowledge of these vast petroleum reserves would likely have made little to no difference to the course of the Second World War. Oil exploration and exploitation is time-consuming and highly technical work. The postwar Libyan oil drilling, even with Italian data, only began exploratory drilling in 1956 and it was not until the early 1960s that the region began producing oil in massive quantities. Companies like Shell or Standard Oil had far more experience than the prewar AGIP and it still took a better part of a decade for the efforts of these companies to bear fruit.

Even assuming that the Italians had magically intuited the correct location for Libyan oil deposits and exploited them earlier, it would have been less of a boon than it would appear at first. Not only would the Italian state have to pour more resources into AGIP, but also the country's refining capacity and tankerage. Libyan oil would still have to be shipped back to Italy, which was problematic given the Royal Navy's categorical superiority over the Regia Marina. An indigenous source of oil might have made the Italian navy more aggressive in the earlier part of the war, but it would not have rectified the serious problems in command, lack of coordination with the air force, and technical problems of its ships that hamstrung the navy in its engagements with the British. DAK might have had more sources of gasoline for its panzers in the theater, but Rommel's general indifference to logistical matters would have meant there simply would have been more jerry-cans of gasoline in DAK supply depots that were not finding their way to the front.

There really is not much to fault the Italians for in their failure to find and develop Libyan oil fields. The colonial and central government did not simply ignore evidence of oil but instead did sponsor judicious geological explorations. It did not help matters that Libya's future oil fields were in areas that needed to first be pacified. This presented a very brief window for discovery, exploration, and then exploitation of what would become a major oil-producing region in the postwar period. The Italians managed to pass the first hurdle, but never quite reached the last two. In the end, the Italians needed both proper equipment and especially time to turn the colony into an oil exporter, and these were two items that were in short supply in 1938.

Sources

Hallett, Don. Petroleum Geology of Libya. Amsterdam, Netherlands : Elsevier, 2016.

Simons, G. L. Libya: The Struggle for Survival. Basingstoke: Macmillan, 1996.