Italy in the 1930s had a plan to turn what is now called Libya into a majority Italian territory. Without the war as a distraction, and with the knowledge of just how much oil is there (another POD), this could be accomplished by the early 1950s. I suspect that Mussolini would offer to take large numbers of Jews from Hitler if they would agree to go to Libya. They would help build up a majority European non-Muslim population. Although a large percentage of them would probably move on later to Israel or the United States, still, they would serve as a "bridge" in building a majority European population. Probably a large chunk of Libya and its oil wealth would be turned over at some point to the indigenous Arab population, but many Arabs would probably choose to stay in the Italian part of the country. The Italian part would become firmly, forever, part of the Italian state and nation, and the oil wealth and enhanced geopolitical importance that this results in for Italy would make it a much more important factor in NATO than in OTL, especially if fascism were reformed from within. Another result would be that the Italian Communist Party would not be anywhere near as powerful in Italy either as an underground force or as a participant in a resurgent parliamentary system.
To keep ALL of Libya as Italian, the Italians would have to forgo the usual settler practice of treating the "natives" as a servant underclass with only limited civil rights, and to make sure they fully participate in the prosperity flowing from the oil wealth. Given the history of Mussolini's treatment of the Arabs in the 1920s and 30s, I doubt this would be possible. Hence the eventual split (after nasty violence on both sides) into two entities, one Italian and one Arab.