The only Tolkien-releated lines in this song are the last two and, of course, the title.

So I'm packing my bags for the Misty Mountains

Where the spirits go now,

Over the hills where the spirits fly.

The Misty Mountains are located near Rivendell and separate the East from the West. I have no idea what spirits go where, unless they are referring to the Gray Havens, where the immortals go once they tire of Middle Earth. (The Return of the King p. 308-310) Note: the Mountains on the eastern boundary of Wales are referred to as the Misty Mountains, having influenced both Tolkien and Plant.