There was a time when The Dreaming had been invaded by two gods, who then conquered the land and imprisoned Dream Of The Endless. Dream begged his siblings for help, and finally Desire sent him a lover to aid him in his battle. The woman, a dreamer, had no name, and so Dream christened her Alianora. Together, Dream and Alianora fought side-by-side and won back the lands from the invading monsters. In the process, Alianora got her trademark scar on her right cheek.
The pair were in love for an unspecified period of time but, as is the pattern for Dream, he eventually grew distant and uncaring toward her. She longed to be away from Dream, but found that she could never truly be away from him because almost everything in The Dreaming is an extension of him. She could no longer return to the waking world, since she had spent so long in The Dreaming that she had been changed by it.
As a compromise, Dream gave her a space of her own; A skerry at the edge of The Dreaming which would be entirely hers and she could populate with creatures from her own imagination. If Alianora ever wished to leave the skerry, she would have to smash the dreamstone which maintained the land, which would summon Dream who would then unmake the skerry, and then grant Alianora any boon she wished that was within his power to grant. (The Sandman: Overture #3)
She lived and eventually died on this skerry, and since then it was passed to many other girls to use as a private escape. The skerry was eventually unmade when Barbie, while under the control of The Cuckoo, smashed the dreamstone and called upon Dream. While he was unmaking the skerry and absorbing all of the land's past inhabitants into himself, a remnant of Alianora reappeared and the two shared a moment together before she too was absorbed into the dream king. (The Sandman #36)
Years later, the ghost of Alianora attended Dream's funeral, and was seen making a speech to the crowd of mourners (though the reader is not actually made privy to what she was saying). (The Sandman #72)