To summarise, two reasons why the Lancaster, and that includes ALL Lancaster marks - and the Lincoln could not have carried out the atom bomb raids on Japan.
1. The Lancaster was not American.
When Gen Groves approached Hap Arnold for AAF support, Arnold read Norman Ramsay's report stating that the Lancaster was the only bomber that could carry Thin man internally but quickly decided that the aircraft HAD to be American. The ONLY choice was the B-29. This was in 1943, two years before the raid took place, when there was no actual mission parameter available.
2. The Lancaster did not have the performance to carry out the mission parameters as they were actually flown.
The Lancaster did not have the range, it wasn't fast enough and could not reach the height the raid was flown at. It is worth remembering that performance figures for Lancasters referred to in official documents and on Wiki or wherever we dredge our crap up from on the net were based on conditions found in the UK at the time of testing, unless otherwise stated. The hot and high temperatures of the mid-Pacific sapped aircraft performance and would have reduced the Lancaster's performance even further.
From the figures calculated by me from official documentation recorded by the Aircraft and Armament Experimental Establishment during the war, to achieve the objective at its maximum take-off weight carrying the bomb (68,000 lb), either Thin Man or Little Boy, but definitely not Fat Man and enough fuel to reach Japan and return, the Lancaster I (Special) would have had to fly at an average speed of 175 mph at an altitude of 15,000 ft across a round trip of approximately 1,700 miles IN TEMPERATE CONDITIONS.
For comparison, at 2am on 6 August 1945, Enola Gay departed Tinian to drop Little Boy on Hiroshima, it returned at 2:58pm after a journey time of 12 hours 58 minutes. The distance travelled was an approximate round trip of 2,722 miles. Using these figures, Enola Gay's calculated average speed was around 216 mph. Loaded with the 9,700 lb bomb and fuel for its mammoth round trip, Enola Gay's gross weight was 140,000 lbs. Little Boy was dropped from an altitude of 31,060ft.
In short, the Lancaster could not have done it.