While I'll leave the detailed exploration of the Libyan oil industry to someone else, the short answer is that Libya at the time produced almost no oil. Mass exploration/exploitation of the country's oil reserves did not begin until the 1950s.

Hence oil availability was one of the (many) shortages for the Italian economy during the war. (Italy being Libya's colonial master at the time.) Vera Zamagni has a good essay on these weaknesses in Mark Harrison's Economics of World War II.