Heat the olive oil in a large Dutch oven over medium heat. Add the lamb cubes and brown them on all sides, about 5 minutes total.
Stir in the onion, carrots, and celery. Cook for 4 minutes until the vegetables begin to soften.
Add the garlic and rosemary sprigs. Cook for 1 minute until the garlic smells fragrant.
Pour in the beef broth and diced tomatoes. Stir in the pearl barley, then season with salt and black pepper.
Bring the mixture to a boil, then reduce to a low simmer. Cover and cook for 45 minutes, stirring occasionally.
Remove the rosemary sprigs. Stir in the white beans and simmer uncovered for 10 more minutes until the barley is tender and the stew has thickened.
Taste and adjust salt and pepper before serving.