Usually, third-person omniscient narration is pretty straightforward. Our storyteller has a bird's-eye view of everything that's happening in the story and can dive down into any character's thoughts at any given time. In The Lion, the Witch, and the Wardrobe, our narrator makes extensive use of this omniscience. Sometimes we focus exclusively on Lucy, such as when she makes her first trip alone into the wardrobe. Sometimes we focus entirely on Edmund, such as when he first encounters the White Witch. Sometimes we leave both of the younger children behind so that we can observe conversations between Peter, Susan, and the Professor. Also, for much of the book, we skip back and forth between Edmund's treacherous journey to the White Witch and his siblings' trip with the Beavers to see Aslan. Sometimes we even see into the Witch's mind, such as when the narrator tells us that she knows the spring thaw means that Aslan is back in Narnia. In fact, just about the only thing our narrator doesn't take time to describe is the final battle between Good and Evil; we only catch the end of that one!
A note of caution: although the narration here is generally third-person, sometimes that pesky first-person "I" does crop up in the narrator's voice. For example, when describing Susan and Lucy weeping over Aslan, the narrator writes, "I hope no one who reads this book has been quite as miserable as Susan and Lucy were that night" (15.8). Even though there are some first-person moments like this one, the narrator of The Lion, the Witch, and the Wardrobe doesn't really have a name or a personality. We like to think of it as a third-person omniscient narrative that stole some first-person pronouns that don't quite belong to it. Alternatively, you could think of these as moments when C.S. Lewis, as he's writing, lets himself peek through the edges of the story and write between the lines.