Well, let's just first start off and say, this isn't actually what happened. Truman did not make any decision, and it was never framed as "the bomb will save lives versus an invasion." This is a post-war justification, and really no historian today thinks this is actually what happened. There was no big deliberation process, there was no singular "decision," there was no trade-off of casualties.

But we can still ask the question about the casualty figures Truman might have heard. As far as we can tell, Truman only had one real discussion about invasion casualty figures. This was with the Joint Chiefs of Staff on June 18, 1945. General Marshall estimated that there would be 63,000 casualties out of 190,000 troops in the initial invasion of Southern Kyushu. Some thought it would be lower. (There was no discussion of the atomic bomb at this meeting.) Now, this was under the assumption that there would only be 350,000 Japanese troops on Kyushu, but by August 1945 they had built up to 625,000 men. A total of 767,000 American troops would be involved in the Kyushu operation.

That's the only documentary evidence we have from the time of Truman being told casualty figures. And hey, those are pretty big — let's not sniff at them. But a) they are far less than the "million plus" figures that people cited in the postwar to justify using the bomb, and b) they are only US combat troops, not Japanese civilians.

In the postwar, the people who took on the mantle of defending the dropping of the bomb (including Truman, Stimson, and others) cited larger and larger numbers. Many of these have come to be repeated as gospel despite the fact that there is no evidence that any of them were discussed at the time. Maybe these people did talk, orally, about bigger numbers, or maybe they just feared them without talking about them. But there is no evidence that they were discussed. They are not very reliable, and they are awfully convenient if you are looking to justify the bombings.

From the best we can tell, this question of casualties — civilian or otherwise — was not a major motivating factor in the dropping of the bombs. Ending the war quickly was, and perhaps those are implicit in that. There were also desires to end the war before the Soviets got too entrenched in Asia, for example. But the idea that it was some deeply considered "lesser of two evils" is not quite right. They didn't see it as an evil at all. They had a new weapon, it was ready to use, they were already targeting and destroying cities regularly, so why wouldn't they have used it? It is only when you are faced with people critical of the bombing that they had to come up with the "agonizing decision" narrative.

Entirely separately, I have never seen any figures from the time that estimates Japanese civilian casualties that would be sustained in the invasion, nor how they would compare to the atomic bombs. There were very little discussions even of how many people they thought the atomic bombs would kill; the scientists estimated around 20,000, it was more like 60-80,000 per bomb. There is no evidence that Truman had this information — it is not even clear he realized that the targets were in fact cities.

On Truman's role in the telling of this story, and some of the criticism of the bombing that came out of it, see here for a brief discussion. On the question of the casualty figures, see Barton Bernstein, "Truman and the A-Bomb: Targeting Noncombatants, Using the Bomb, and His Defending the "Decision'," Journal of Military History 62, no. 3 (July 1998), 547-570.