The 1st batch of P38s were meant for the British who ordered them for some reason without superchargers and the props both rotated the same way. Lockheed called this version the castrated P38.
The first "batch" of P-38's were not meant for the British. The P-38 was an American design, for the USAAC, before the British considered it. The British did get on board early as the P-38 shared some parts commonality with other US aircraft the British were already flying.
The very first P-38, the XP-38 (37-457), had counter rotating props, from day one, and had them from well before the aircraft was ready to fly. The counter rotating props on the XP-38 rotated inwards. This is well documented.
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Below is a picture of the XP-38. You can clearly see, by their pitch, the props are counter rotating, and rotating inwards.
The first P-38's ordered by the Army Air Corp were the YP-38, and they had counter rotating props, rotating outwards, to improve stability in comparison to the inwards rotating props of the XP-38. All American P-38's from that time on had the props rotating outward.
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Below is a picture of a YP-38. You can see by their pitch that the props are counter rotating and rotating outwards.
The YP-38 was being built for the US and the P-38, P-38D, and the P-38E were ordered by the US before the British and French ordered the 322B and 322F. The 322B (the British model) was the first model with props that rotated in the same direction.
The P-38 was designed with counter rotating props, and the US took delivery of several aircraft before the British ordered the aircraft with props rotating in the same direction. The British ordered the aircraft with one motor type only, and props rotating right handed, to simplify the supply chain as this matched their existing requirements and parts supply for P-40 Tomahawk aircraft (using the same engine). They were ordered without turbosuperchargers as they were envisioned to be used in a different role, primarily at lower altitudes.
As I said, the British and French versions were not using counter rotating props, but all others did, and the aircraft was designed with counter rotating props from very early in the project. The British and the French changed the design themselves (not a Lockheed change) to simplify the supply chain.
For timelines (roughly, from memory so there may be some minor errors in date but not general timing):
The P-38 specification was let in 1937 (some say initially late 1936). Lockheed won and was awarded the contract to build the XP-38 in June of 1937. The XP-38 (already with counter rotating props) flew in late January, 1939. The XP-38 crashed in early February, 1939. The USAAC ordered YP-38's (with counter rotating props) in April, 1939. The YP-38 first flew in September of 1940. In September of 1939, a year before the first YP-38 flew, the USAAC ordered 66 production P-38's (all with counter rotating props), about 30 were to become "P-38's" and about 36 were to become "P-38D's". Orders were placed for the P-38E (with counter rotating props) before delivery of the YP-38 was complete. The first P-38E rolled off in October, 1941.
The British ordered the model 322 Lightning Mk 1 (a modified P-38E without turbocharger and with motors rotating in the same direction) in March 1940. The P-38E would have been the third batch of P-38's (after the YP-38, P-38, and several experimentals), and the 322 would have been the 4th batch or it might be considered the third batch as it was concurrent to the P-38E. The first Lightning I's arrived in England in March of 1942. So, before the British ordered the 322B with right handed props, the XP-38, YP-38, P-38, P-38D, and P-38E had all been ordered or planned, and several flown, with counter rotating props.
Lockheed had a lot of issues with the plane and the contra rotating props pointing outward as I stated helped to reduce the effects of torque and make the P38 more stable in flight. The advantage of such designs is that counter-rotating propellers balance the effects of torque and P-factor, meaning that such aircraft do not have a critical engine in the case of engine failure.
In designing the P-38, the decision was made to reverse the counter-rotation such that the tops of the propeller arcs move outwards, away from each other. Tests on the initial XP-38 prototype demonstrated greater accuracy in gunnery with the unusual configuration.
Errr....no, the XP-38 did not demonstrate greater accuracy with the "unusual configuration" of props rotating outwards. The single XP-38 had counter rotating props (from day one) that rotated inwards, not outwards. The XP-38 never had props rotating in the same direction, and never had props rotating outwards. It only flew with counter rotating props rotating inwards. The XP-38 crashed (16 days after it first flew) before any changes to rotation were tried. The very first YP-38 had props that rotated outwards.
There were several "issues" in designing the P-38, there almost always are in major new aircraft designs. But in regards to T and P factors it makes little difference if the rotation is inwards or outwards, both rotations are roughly the same with regards to P and T factors. The flow towards the outboard wing panels, vs the inboard panels, did make for greater stability at lower speeds, but no real change in P or T factors.
T!