Let me explain. There was a lot of left-wing agitation within the Kingdom of Italy during the Biennio Rosso from 1919 through 1920. In a world where this has led to a successful socialist revolution in Italy during this timeframe (this would probably be more likely had the Revolutions of 1917-1923 successfully established communist rule in places like Germany, Hungary, etc), what would have become of Italy's Libyan colony?
Could the monarchy, military, and socioeconomic elite have successfully fled to the colony and established it as a rump state for the Kingdom of Italy, in the same way that Chiang Kai-Shek's Chinese Nationalist forces were able to evacuate to Taiwan after the Mao won on the mainland? Was the infrastructure in Libya have been in place for such an evacuation? Or would it have been more likely for the colony to be seized by the new left-wing Italian government, or by another colonial power like Britain or France?