I read somewhere else that C. S. Lewis defended accusations that he was writing "allegory" by saying that he was merely exploring how Christ might have incarnated in a world like Narnia. Fair enough. Although you can't really say that Aslan's Christ is a different Christ from Jesus' Christ so the application of Aslan's behavior to our world is direct (although Aslan implies that the children mush learn to understand him under "a different name" at The Voyage of the Dawn Treader.)
I think a slight extension to Lewis' description, above, would be that Aslan explores what the world would be like if Christ actually returned to Earth and hung around. There is no Holy Spirit as intermediary here. Aslan bails people out and advises them in the flesh, not as some feeling or strangely-warmed heart.
Perhaps this exactly what Lewis intended and makes this clear somewhere else.