The narrator of The Return of the King knows everything, from the names of the orcs that imprison Frodo (Shagrat and Gorbag) to the deep confusion Éowyn feels over her sudden attraction to Faramir at the Houses of Healing. Not only is this narrator all-knowing within the novel, but the narrator also has complete knowledge of the mythology and genealogy that supposedly exists outside the novel: witness the extensive "appendices" that follow the main action of The Return of the King. We're definitely going with "omniscient" narrator on this one; what is more, since the narrator isn't a character within the novel and never speaks directly to the reader, this is a third person, more objective-seeming perspective.
What's so great about Tolkien's use of an omniscient narrator is that we really get a sense of Middle-earth as, well, an earth. It's a world unto itself, and we get access to every nook and cranny of it. Cool, huh?