I got some more on the bird shown in your photo.
A P-38G was captured by Regia Aeronautica when, due to a malfunction of the compass, landed by mistake in Sardinia on June 12, 1943.
Later the P-38 was flight transferred to the test center located in Guidonia (near Rome) and painted with Italian markings.
The aircraft was also scrambled a few times in August 1943 by Colonel Tondi and, on August 11, she attached and shot down the B-17F s/n 42-30307 belonging to 419th BS, 301st BG.
Later, the aircraft was grounded because Italian gasoline was too corrosive for her tanks.
About the markings, I'm still searching but, as seen on captured French aircraft, the majority only received the markings shown in photo: white Savoy cross on the fin/rudder and white fuselage band.
Cheers
Alberto