This was one of Dylan's most public displays of affection for his then-wife, Sara, who he married in 1965. At the time of writing, the couple were on the brink of divorce, and this was Dylan's attempt at reconciling with his "radiant jewel, mystical wife." Despite the attempts to make amends, Bob and Sara would ultimately divorce a year later in 1977.
Dylan reveals that he wrote "Sad Eyed Lady Of The Lowlands" for Sara in this song: "Stayin' up for days in the Chelsea Hotel/Writin' 'Sad-Eyed Lady of the Lowlands' for you."
Sara actually showed up at the studio and listened to Dylan record this song. Jacques Levy, who collaborated on much of the Desire album, is quoted in Bob Dylan: The Complete Album Guide as saying, "You could have heard a pin drop. She was absolutely stunned by it."