Reports from the time had an American Invasion resulting in the loss of ~41,000 American lives, while the bombs produced 200,000 deaths. I know the casualty numbers greatly favored the US in the War in the Pacific, but is it possible that the bombing saved Japanese lives?
I'll jump in.
It's quite possible, almost to the point of certitude, that the bombs saved millions of Japanese lives.
When the Pacific War actually ended, it took nearly $1billion (1945 dollars) worth of donations in food, medicine and supplies to keep Japan from famine. It took nearly two years for Japan's infrastructure to recover from the damage caused by the US ships and planes and be able to actually feed its own people more or less unassisted.
If the War hadn't ended when it did, millions of civilians would likely have starved to death during the winter of 1945/46. Never mind the military casualties from the impending invasion of Kyushu and, later, the Kanto Plain.
So, yes, an argument can easily be made that the dropping of the atomic bombs saved lives.
Further, your suggested loss of "~41000 American lives" is much too low. I've seen reports of that many in the first month, and as many as 800,000 for the entire conquest of Japan.