It did not save American lives, but it did terminate many innocent Japanese lives.
Yes, it saved American lives. Who knows how many thousands. Japanese were killing themselves wholesale, including civilians. They refused to surrender, some would strap bombs on themselves and run into our forces. Groups would charge with pitch forks. Just one determined suicidal zealot can do a lot of damage.
Watch the show "World War 2 from Above". I saw it yesterday and leaves all doubt that it was the right thing to do. I learned a lot. One interesting thing is the cost of the atomic bombs. Over 600,000 people were employed and the cost was about 25 billion in today's money. One of the reasons it was so expensive was they weren't sure which would work, plutonium or uranium so they developed both. Fat Boy and Little John were different, they both worked.