There is a unit history of the 39th here:
http://usafunithistory.com/PDF/30-49...INING%20SQ.pdf
Pages 10 and 11 concern combat in May, including May 20th. For what it is worth a couple of lines in the report may be of interest. An anonymous 39th pilot who kept a personal record of the early operations, wrote of the day and these appear to be comments from that pilot.
"Lts. (Green), Adkins, Lynch, Wahl and Carey the first of our Sq. to participate in combat activities in New Guinea."
"One of the pilots, Lt. Tom Lynch, was destined to become a great ace of the Pacific war. He was also the rare sort of pilot who naturally took to leadership position."
"One of his traits was that he only claimed victories which were absolutely sure kills. His score would have been much higher if he had claimed every enemy plane that may have gone down before his guns. Another remarkable fact was that he scored three of his victories in the Airacobra."
On May 20, Tommy Lynch scored the first victories for the Squadron. Whatever the result of the combat, the 39th journalist recorded some telling attitudes about the weapon at hand (the P-39):
"Lts. Lynch, Wahl, and Adkins, flying in a 5-ship flight in cooperation with the 35th Sq., 8th Pur. Group,
intercepted 6 Zero fighters at around 15,000 feet. When first sighted, the enemy, who were flying
loose echelon, observ· ed our head·on attack. Lt. Lynch reported hits on 2 E/A but no results were
determined. After attack E/ A pulled around on our planes' tails and our pilots dived away. Lts.
Wahl and Adkins reported no results. Enemy casualties were probably 2 Zeros. Our casualties had
Lt. Lynch's plane shot up but landed safely. Lt. Carey bailed out of plane and was injured when he
hit the ground." Comments: Lt. Adkins: "Could have done better with a truck; it's more
maneuverable and will go higher."
Lt. Wahl: "Could have done damn good with altitude ship."
"Apparently, Lynch was granted confirmation of two victories probably on the basis of wreckage identification of the Zeros in the
jungle."
I read this to mean that the hits Lynch claimed on the first two "results undetermined" zeros were later "confirmed" to be shot down. There was not a second flight on the 20th.