Given Lyra’s position, a quick military inquest was the best choice.  They could be convened anywhere, so Lyra wouldn’t have to leave Ponyville.  Celestia would have to recuse herself, of course, since she’d been the one to issue the orders, so Luna would have to preside.  Everypony thought Luna was cold-hearted but fair, which would work to her advantage—nopony would be second-guessing the verdict.  Shining Armor, as captain of the guard, would of course be Lyra’s advocate, and she could probably persuade Fancy Pants to act as a civilian barrister.  All the upper-class unicorns loved him, and they’d hang on his every word.