According to the Bible, all have sinned and need forgiveness, sin brought death into the world, and Jesus' death atoned for the sins of the whole world. Many characters in the Chronicles aside from Edmund also sin, but Aslan's death is primarily discussed as being for Edmund's salvation based on the Deeper Magic from Before the Dawn of Time. Was in the cause of death in Narnia as in our world? Did the other Narnians also need atonement for their sins, and if so, was this brought about through the death of Aslan? I know that the Deeper Magic made death work backwards, but I am not sure if that refers to death in general or specifically to Aslan's death.
@kj7rrv I think this is one of the places where it becomes clear that the Chronicles of Narnia are not allegory and are also not intended to be a sort of "Christian Theology 101" class in children's book form.
Lewis wasn't attempting to make every single aspect of the Narnia stories correspond directly with something from the Bible, or from Christian theology or the history of Christianity. Trying to force the books to fit a consistent theological plan just does not work.
Aslan's sacrifice of his life to save Edmund (and his resurrection afterwards!) is certainly meant to remind readers of Jesus' death and resurrection, and the fact that Aslan does this selflessly for the sake of one person is meant to make us think of the one who laid down his life in our world for the sake of every individual, including you and me. But there's not a direct one-to-one correspondence in terms of theology and doctrine. We indeed aren't told that Aslan's sacrifice is for the atonement of all Narnians' sins — although it could fairly be said that he saved them all from the White Witch by destroying her. There's no explanation either of what "Death itself would start working backwards" means, beyond the fact that Aslan himself has come back to life.
And then in The Magician's Nephew, which was written a few years later as the prequel and has some major and irreconciliable inconsistencies with The Lion, the Witch and the Wardrobe, we likewise don't have direct parallels with the Biblical accounts of Adam and Eve and Satan and the original sin and so on. Hints and allusions, perhaps, but they're general and don't ever correspond exactly, and they're not supposed to.
Basically, Lewis didn't plan out any sort of theology of Narnia and write the books to fit that plan (or any other kind of plan, despite what some commentators have tried to read into the series) — so there is really no point in reading the books with the thought of figuring out the Narnian equivalents of any points of Christian doctrine. It's honestly better just to read them and enjoy them for what they are.
"Now you are a lioness," said Aslan. "And now all Narnia will be renewed."
(Prince Caspian)
Petition to preserve the gender of Aslan in Greta Gerwig's upcoming Narnia film
(because Aslan ISN'T a lioness!!!)