The auction house Profiles in History expects the lyrics to sell for more than $200,000.
The document has the opening lyrics and a rough sketch of four people in a room with windows draped in curtains.
Lennon said the song was inspired by his son Julian who, as a child, drew a picture of his classmate Lucy and told his father, "That's Lucy in the sky with diamonds."
Lucy Vodden, whose maiden name was O'Donnell, revealed in 2007 that she was the Lucy named in the song.
She died in 2009.