In Deathly Hallows, the Death Eaters kidnap Luna to stop her father Xenophilius publishing more provocative Quibbler issues. Harry, Ron, and Hermione learn this when they visit the Lovegood house, ending in Xenophilius unsuccessfully trying to hand the trio over to the Death Eaters. They assume the kidnapped Luna is in Azkaban (“probably teaching the other inmates about Nargles and Crumple-Horned Snorkacks”).
They later hear on Potterwatch that Xenophilius’ failure to turn them in has landed him in Azkaban.
Later, when the Snatchers capture the trio, they take them to Malfoy Manor, where Voldemort has set up headquarters. When the trio is thrown into a cellar, they find themselves sharing a cell with Mr Ollivander and Luna.
Ollivander has been kidnapped to provide Voldemort with information about wandlore—especially the connection between Harry and Voldemort’s wands—so it makes sense that he should be kept close at hand, rather than in Azkaban.
But why was Luna kept at Evil HQ, Malfoy Manor, rather than thrown in Azkaban?
She doesn’t seem to have been of any particular importance to Voldemort directly—the whole point of abducting her was just to silence her father. If Xenophilius was just thrown in Azkaban, why was Luna different?