The Germans did investigate nuclear weapons, but the Nazi race policies meant that the brain drain of worthy and knowledgeable scientists deprived them of the expertise required. Thankfully, the likes of Leo Szilard and most notably Edward Teller benefitted the Manhattan Project enormously. That alone and the effort made to produce and refine the fissile material for a workable bomb was a huge effort that the Germans just did not have the resources or knowhow to do accurately within the timeframe of the war.
Refining uranium and the production of plutonium, an isotope of uranium and not found naturally except from refining uranium, is an extremely exact science. The US (rather, Multinational as there were scientists from all over the world, including little ole New Zealand involved in the Manhattan) project had difficulty doing this for their first aerial bomb, the Thin Man, a gun type weapon, which led to its cancellation when the plutonium being produced at the Hanford Site in Washington State was full of impurities and there was a fear it might not produce a chain reaction.
In a hypothetical scenario, the He 177 might have been possible to carry such a device, but at what cost? The He 177 was unreliable and the in service models were plagued with serviceability issues. Perhaps the He 274 might be a better bet, but again, a lot has to happen before that gets near production, like no Operation Overlord, for example as that aircraft was built in France. The best weapon the Germans have for delivery of a nuclear device is far and away the V 2 and any future projects (since we are speaking hypothetically), such as the A 10. Regardless of its lack of accuracy, it's unstoppable once it launches, but there is also the unreliability of the technology that comes into play as not all V 2s that were launched actually survived the forces on them during flight. The Germans, had they gotten that far would have made sense to deploy a nuclear bomb on a rocket rather than an aircraft.
The Black Lancaster's were trained as a back up for the Bomb delivery.
IF, and that is a BIG
if that such a thing even existed. The original source might be a book on airfields in Oxfordshire under the listing of RAF Enstone with little substantial fact behind it. Mark Felton's youtube video is riddled with inaccuracies, which lets his otherwise interesting take on the subject down - and I wouldn't rely on the Wiki page on Enstone, which references Felton's video - eek!
Let's put it this way, the Lancaster was listed as the only aircraft that could carry the Thin Man bomb internally, but both Groves in charge of the Manhattan Project and Gen Arnold expressly stipulated an American type. The Lancaster was
never considered for carrying either Little Boy or Fat Man operationally by the Americans. Dr Ramsay, who suggested the Lancaster in his 1943 report proposed that it might be available for trials, but again, Arnold rejected the proposal for the same reason as earlier.