I can understand calling it the Lightning but not the II suffix. We don't do that.
Anorak here. By rights the F-35 should be the Lightning IV. The very first Lightning was the P-38, though an American aircraft the name was bestowed by the British, in British service to be known as "Lightning Mark I", and a one off P-38, "Lightning Mark II". For the US the F-35 is indeed a Lightning II, as they never enjoyed
newt's Lightning Mk. III except by way of exchange.
