OP2: >> "...saved a lot of allied lives..."
The atomic bombings of Japan had nothing to do with the military campaign in the Pacific theater, which by 1945 had been decisively and indisputably won by the Americans. They had literally run out of targets to bomb in the Japanese home islands. [0-1] An argument could be made that the Atomic bombings saved some American lives by accelerating VJ day and thereby precluding some unpleasant island-hopping, though I've never been terribly convinced.
The atomic bombs were about scaring the Soviets, plain and simple. By '45 the American military was perfectly aware that it had won the Pacific, would soon win the European theater, and had long since turned its attention to preparing for the cold war and plundering German technology and other assets.
[0] See for example Sec. of War Henry Stimson's diary and papers, which are excerpted here among other places: http://www.doug-long.com/stimson5.htm It might help to command-F down to this quote: "I was a little fearful that before we could get ready the Air Force might have Japan so thoroughly bombed out that the new weapon [the atomic bomb] would not have a fair background to show its strength."
[1] https://en.wikipedia.org/wiki/Air_raids_on_Japan#Attacks_on_...