In Virgil's epic The Aeneid, Lavinia of Latium is a minor character. She doesn't even show up until the last six books of the poem, and when she does arrive, it's to serve as a sub-par Helen Of Troy, driving men to battle simply by what she represents. Aeneas needs to marry her to secure his position in a strange country, while Turnus, a local king, isn't willing to step aside for a group of foreigners. The epic ends with Aeneas slaying Turnus in a rage after Turnus surrenders to him. There's no mention of the wedding that must've followed, the life Lavinia would've had with the stranger who basically conquered her country in pursuit of her, or what she felt about any of it.
Which isn't Virgil's problem—it's a long poem, but there's a lot of ground to cover, and the feelings of one teenage pawn are easy to overlook. In Lavinia, Ursula K. Le Guin's elegant homage, the title character takes center stage, narrating the events that lead to Aeneas' arrival and the war, then going past The Aeneid to show the foundation of Aeneas and Lavinia's city, his eventual death, and the fates of their children. Le Guin explains the complicated relationship Lavinia has with her mother—driven near-mad with grief over the death of her sons—and her father, a loving, supportive parent who pushes aside his responsibility at the moment where strength is needed most.
The trickiest part of writing a novel in the shadow of such a well-known work is justifying the existence of something that could easily be dismissed as just a higher-minded version of fan fiction. Le Guin, a justly revered author in her own right, handles this by directly acknowledging Virgil's poem; Lavinia meets the poet's dying shade while visiting a forest shrine, and he tells her future in a series of haunting, elegiac dialogues. There's a strong indication that the Lavinia in Le Guin's book is the one from Virgil's poem—that she and the world she describes are a living fictional construct that exist because of the poet's creation. It's the sort of playfulness that could've come off as gimmickry, but in Le Guin's capable hands, it creates an extra layer of life.
Lavinia succeeds largely because its author approached it with no greater intention than paying tribute to a source material she found deeply inspiring. Le Guin's usual concerns—the vagaries of fate, the necessity of balance—never feel shoehorned in, and the result is a book that honors its source while being fully satisfying as a standalone. It's good for the soul, really; two masters dueting over a 2,000-year gap without ever missing a note.