Don't get me wrong, I love the Lightning, but I don't think it would be a likely candidate for Mossy replacement in the eyes of the Air Ministry unless they are strictly looking for something in the Heavy fighter role. The Mosquito was a fast/light bomber, first and foremost, and was well adapted to other roles; the P-38 was a Fighter/Interceptor first and was then adapted in other directions. They both crossed over into being superlative pathfinder and recce platforms and although the P-38 was a good tactical bomber/CAS platform and was adequate as a night fighter later in the war the load over range capabilities (as well as the multi-seat configuration) of the Mossy made it the better bomber and night fighter. If the RAF wanted a true replacement for the light bomber / multirole airframe I think the Douglas A-20 (P-70 as Night Fighter) is the most likely American platform to adopt, later followed by the A-26--but neither of those make effective fighters and they are both considerably slower than the Mosquito, so there's a trade-off.
I just don't see any other allied plane that could realistically be fielded by 1942/43 even that could offer a true replacement for the Mosquito. The P-38 is the only one that comes close but they would have to give up rage for payload on bombing raids.