I had always accepted the argument that the atomic bombing of Japan saved lives that would have been lost in a ground invasion, but a history professor told me recently that the Japanese had already offered to surrender and that it was necessary. I have never heard this before and was suspicious because if this is true I don't see why the issue is so controversial. Thanks.
The short version: the Japanese high command was not of a single mind. A minority, but an important one (it included the Emperor, the Foreign Minister, and other top figures) wanted to find a way towards a diplomatic end of the war. They hoped that the Soviet Union, which was neutral with regards to Japan up until that point in the war, would serve as an intermediary with the other Allies to press this point. Their goals from this diplomatic overture are not entirely known because, as we will see, they never got to actually make it. But the outlines are that they were especially keen to have the "unconditional surrender" requirement modified, with the major sticking point being the disposition (or lack of clarification on it) of the Emperor and the imperial house. They were worried that "unconditional surrender" might open Hirohito up to being arrested or deposed, and the imperial house destroyed, and they considered that completely unacceptable (to put it in American terms, it would be like saying you would shred the Constitution — what would the United States be, if you did that? Not the same country).
The Americans knew the Japanese were doing this because they were intercepting and decrypting the communications between their Foreign Minister in Tokyo and their Ambassador in Moscow (the MAGIC intercepts). But the Japanese did not make this offer directly to the Americans.
The Soviets were interested in entering the war against Japan, having been asked to do so by the Americans, and seeing possible seized territory as the benefit for them (notably the entirety of Sakhalin Island and the Kuril Islands, which would give the Soviets easy access to the Pacific Ocean through Vladivostok). So they strung along the Japanese ambassador.
Finally they met with him on August 8th. As he prepared to go into a discussion about his desire regarding the Soviets interceding with the Allies, the Soviet Foreign Minister instead handed him a piece of paper that said that the Soviet Union was declaring war on Japan. Soviet forces started pouring over the border into Manchuria within hours.
The Emperor issue did not just go away. The Japanese essentially offered to surrender on August 10th, the day after the Soviet invasion and the bombing of Nagasaki. But they still held out the condition of the Emperor's disposition. The Americans indicated in no uncertain terms that "unconditional" meant "unconditional." Finally, on August 14th, after an attempted coup, the Japanese indicated that they would accept that. In the end, the Americans decided to preserve the imperial house anyway, but to make it more symbolic than functional.
So there are those who argue that the US could have mostly gotten what it wanted without two atomic bombs, or without the Soviets entering the war. But it's not an easy thing to parse out, since we don't really know what the Japanese demands would have been beyond the Emperor's status being clarified.
Separately, though, the idea that it was just a choice between "drop two atomic bombs on cities" and "launch a ground invasion" is not how it was framed at the time, nor the only two options on the table. I have written a bit about other "alternatives" that were discussed at the time here. The strategy of pitching it as the "lesser of two evils" is a deliberate attempt (by the people who were justifying their use of the bombs in the postwar) to frame it as a false dichotomy. The historical record shows more complexity than this. This doesn't mean you have to think the atomic bombs were not "justified" — but don't fall into the "trap" of the "either/or" reasoning.