Dana had been unaware of this and so was I.
Here is a bit of info I cut and pasted from Wikipedia (in lieu of actual research):
The song's lyrics were heavily influenced by The Lord of the Rings by J. R. R. Tolkien. The opening line ("Leaves are falling all around") is probably a paraphrase of the opening line of Tolkien's poem "Namárië". The poem may also be the inspiration for the entire first verse.
The Tolkien references later in the song refer to abstract themes - Mordor, "girl so fair" the ring - without specifically invoking Tolkien canon:
Mine's a tale that can't be told,
My freedom I hold dear;
How years ago in days of old
When magic filled the air,
'Twas in the darkest depths of Mordor
I met a girl so fair.
But Gollum, and the evil one crept up
And slipped away with her.
References to the work of Tolkien also exist in other Led Zeppelin songs, such as "Misty Mountain Hop" and "The Battle of Evermore". Some speculate that "Stairway to Heaven" also references Tolkien.
Here's a video from YouTube that combines "The Battle of Evermore" with clips from the movie.