How did Truman justify the use of the Atomic Bomb?

Answer: his chief priority was saving American lives.

Explanation: He was president of America not Japan and he didn't know how close the Soviet Union was to making their own bomb. Or how close and his advisors told him that if an attack from Japan were to happen, it'd cost over a million of American lives.

Truman justified the use of the Atomic Bombs by claiming more American lives would have been lost in an invasion of Japan. He concluded that more lives had been saved with the use of the Atomic Bomb. It is still argued whether this would have been the case.