The story is more grim and heart-wrecking.
And there is no obvious take-away, everything just sucks.
But it's a story of a loss that one can relate to. Depressed people are known to listen to sad songs, and get relief from that.
I'm not in a very good place now, and reading the Lion and the Puppy story in Russian somehow was a relief. It melted the numbness away.
And that's what Tolstoy was going for, perhaps. No ham-fisted morals. Just carefully crafted vignettes of grim life.
I do think that Tolstoy never had an appreciation of the many dimensions of human happiness. "Every happy family is alike, but unhappy families are miserable in their own ways", he wrote. I disagree; I see commonality in misery, and it's the path to happiness that has to be crafted and often ends up unique. But I digress.