Heat the olive oil in a large Dutch oven over medium-high heat. Add the lamb cubes and brown them on all sides for about 6 minutes. Remove the lamb and set it aside.
Lower the heat to medium. Add the onion and cook until it softens, about 4 minutes. Stir in the garlic and cook for 1 minute more.
Pour in the apple cider and scrape the bottom of the pot to release any browned bits. Return the lamb to the pot along with the chicken broth, salt, and pepper.
Stir in the pearl barley and bring the mixture to a simmer. Cover and cook for 30 minutes, stirring once halfway through.
Add the parsnips and continue simmering, uncovered, for 25 minutes until the barley is tender and the parsnips are soft.
Stir in the chopped sage and cook for 2 minutes more. Taste and adjust salt if needed before serving.