They did not save any lives, that is a completely made up invention. In fact Imperial Japan cared little about the atomic bomb, and even if a land invasion had become necessary, the USA had made a deal with the USSR to invade on land.

This was the real reason for the bombings, not to beat Japan into submission, which Roosevelt's deal with the USSR for a land invasion ensured, but to show the USSR the destructive power the US held. Truman was a staunch anticommunist, and refused to let the USSR play the part Roosevelt negociated in a land invasion.

It was a war crime with no benefits at all except to show off to the USSR, who would develop nukes themselves 4 years later anyway. An absolute tragedy which proved to be entirely useless.