Libya's population is small enough, that any retention by Italy would result in it being Italian majority and part of Italy.
Ehh I wouldn’t say that, Libya still has 6 million people today? Even if you have better quality of life resulting in a slower growth (or is it? when comparing with another developped country with an Arab population - Israel, israel’s Arab population doubled between the first intifada and 2010 (Israel then put heavy immigration restriction for Arabs-Palestinians, during that same period the Libyan population growth was only 60%, by comparing 1955 and current TFR the Arab Israeli one in consistently 20% higher, i should look into it more but I can imagine the feeling of « competition » may explain part of this, I’m sure Arab Israeli did live better on average than Libyan pre Civil war.
Even if we assume a slightly smaller natural population - 5 millions that is still quite a lot, would some emigrate because Libya, controlled by Italians lack opportunities and they would go to mainland Italy? Sure but i’m Not sure it would be enough , it seems 14% of the East German population left to West Germany between summer 89 (when there was a reduction in patrol around the border) and the mid 2000s, , even if you assume a constant 1% (similar to East Germany in the years following reunification, so pretty high) migratory flow to Italy for 70 years that still only halves the population , you still have 2.5-3 million Arabs. Would the same number of Italian settle there? French certainly had trouble settling Algeria in the long term, with pied noir population stagnating between 1930 and 1954, now there is was an economic incentive to leave Algeria since wage were 20% lower there, but I’m not sure a democratic Italian government post-Mussolini (say post early 70s, with him dying in the late 60s and a few more year of dictatorship Portugal - style) would necessarily do large scale effort to send Italians there, so there need to be a multiplication by close to 20 of the Italian in 1940-1975 if we want them to at least overcome Arabs (assuming something like a 50-100% growth from the oil economy after 1975 for them to number 3-4 millions, which is already optimistic), that’s possible, Portugal sent 1 million in less time and with 6 times less people, but it still would require a coherent plan, no significant insurgency near urban Centers and some incentive to go there, especially before oil is discovered, there is a target in migrating south Italians there who would gladly leave , it seems 2 million Italian left Italy between 1929 and 1975 (mostly from the south), while redirecting all of these seems impossible maybe it is possible to redirect a third, half? And it would be complemented by internal migration from the northern part of the country because of opportunities in the oil industry. There were huge development of Libya in the 30s, and there were 20,000+ settlers per year in 1938-1940, during the time Italians “flocked to Libya”, they would need 3 time that number , 60k to hope to reach a similar population as the Arabs by the 70s and the fall of the regime. Possible but I wouldn’t call it certain
It seems thight but possible, there would not be an overwhelming majority in any case , but it would require significant subsidies and a stable plan for settlement of Libya under the dictatorship, a quick pacification of it, you also have to hope Libyans Arab don’t Purposely have many children to compete with the Italian invader (Palestine or Quebec style)
But I wouldn’t say it happens in *every* timeline where Italy keeps it.