The original Cupid and Psyche story comes from Lucius Apuleius's The Golden Ass, which is, for lack of a better term, an ancient novel, that is, an extended prose narrative following the adventures of a single hero. Its actual name is the Metamorphoses, which hints at Ovid in the background, but it is often called The Golden Ass, or Asinus Aureus, because it was the name given to it by St. Augustine, who knew it quite well; the name comes from the fact that the main character manages to get himself turned into an ass for a considerable portion of the narrative. Much of the story is extraordinarily lewd, with all sorts of sexual shenanigans, but it occasionally slips into the philosophical, using physical transformation as a symbol of moral transformation; and throughout the story there are digressions in which people tell other stories each of which still touches on the underlying theme of transformation. This format, which may or may not have originated with Apuleius himself, influence much of later storytelling, of course. Of these secondary stories, the tale of Cupid and Psyche stands out because it is so radically different from the rest of the work -- whereas other secondary stories, and, indeed, much of the rest of the novel revels in sexual buffoonery and farce, here the theme of transformation takes on a different tone entirely. It's not that the sexual element is missing: Cupid is, after all, the god of erotic love, and there is sexual humor of a somewhat subtler sort (e.g., Cupid goes on strike, and everyone starts complaining about how boring things have become), and the daughter of Cupid and Psyche is Voluptas, who is the goddess of sexual pleasure. But the story itself is strikingly high-toned and lacking in buffoonery, with the allegorical overtones carried by this sort of myth (psyche is, after all, the Greek word for 'soul', what makes you a living thing; and eros, desire, has a long philosophical history, as anyone knows who has read Plato's Symposium). What is more, this is almost certainly deliberate: the story occurs right in the middle of The Golden Ass, and in a sense anticipates the religious character of the final book, in which the protagonist, Lucius, begins to be inititated into the rites of the goddess Isis.
Lewis had long been toying with the idea of a version of the Cupid and Psyche tale told through the eyes of Psyche's elder sister; she is in some ways the villain of the story, since she pesters Psyche to do things she shouldn't do, and which result in a great deal of suffering. He could very well have gotten the idea in part from William Morris's telling of the story in The Earthly Paradise; and the young Jack Lewis shows an interest elsewhere in retelling myths from the perspective of the villains and monsters, the sort connected with Promethean Romanticism. He dabbled in some poetic attempts, but not much came of it until he actually started working on a prose story in the 1950s, which he titled Bareface. He could not convince the publishers that this was a good title for a book (they said it sounded like it was a Western!), and eventually went instead with Till We Have Faces, from the single most important line in the book, which Orual says of the gods: "How can we meet them face to face till we have faces?" The book explores the theme of love, of course, both pure love and love that has become sick and devouring; and it explores the intersection of reason, cool and clear and bright as water, and imagination, warm and dark and earthy as blood; and it explores the agonies of religion, with its blood and dark places and terrible events that the gods rule but for which they never answer; and it is about self-knowledge and the lies, and truths, of reason and imagination alike, that is, it is about human faces; and it is about betrayal and death and reconciliation.
One of the things that has always intrigued me is Lewis's epitaph for the work: Love is too young to know what conscience is. It comes from Shakespeare's Sonnet 151:
Love is too young to know what conscience is,
Yet who knows not conscience is born of love?
Then, gentle cheater, urge not my amiss,
Lest guilty of my faults thy sweet self prove.
For, thou betraying me, I do betray
My nobler part to my gross body's treason;
My soul doth tell my body that he may
Triumph in love; flesh stays no farther reason,
But rising at thy name doth point out thee
As his triumphant prize; proud of this pride,
He is contented thy poor drudge to be,
To stand in thy affairs, fall by thy side.
No want of conscience hold it that I call
Her ‘love’ for whose dear love I rise and fall.
It, like the original Cupid and Psyche story, is a poem that can be read in a bawdy or non-bawdy way, as you please. But I suspect the connection here is chiefly that posited between conscience and love in the first two lines: love must find fruition in conscience, but conscience cannot be had unless we first love.