It's Italian, so not under direct German control in the 1930s; Mussolini didn't want a war in 1939, and wouldn't have been planning the (extremely expensive) infrastructure buildup this would require (not just to drill the wells, but to transport the oil to the ports, and from the ports to Italy proper). Libyan ports famously had issues supplying the Afrika Corps during the war; now we also have to add in developing them enough to ship fuel back to Italy (and ignoring the fact that they would be extremely tempting targets once the war broke out; British submarines would feast on Libyan oil shipments, and there would certainly be at least some planning done for raids on the docks themselves, even if they proved infeasible in practice).
More broadly, the oil still has to get to the front lines, which means Germany still runs into the same logistics issues. By the time the oil situation became critical OTL, the USSR had already managed to halt the 1941 German advance, and would be able to do the same for 1942, even if in a less stunning fashion than Stalingrad. Meanwhile the US is still producing everything at a rate the Axis can't hope to reach (and Italian oil does absolutely nothing for the Japanese, who really need the oil the most).