Sprinkle lamb with salt and pepper. Heat a large nonstick skillet over medium-high heat. Add lamb; cook 12 minutes, browning on all sides. Remove from skillet. Add carrot, onion, and celery to skillet; sauté 3 minutes. Add wine. Bring to a boil; cook 5 minutes. Stir in broth, rosemary, tomatoes, and bay leaves. Return lamb to skillet (skillet will be very full). Cover, reduce heat, and simmer 2 hours or until lamb is very tender, turning lamb once. Remove lamb from skillet; bring liquid to a boil, and cook 5 minutes. Discard bay leaves.
Sort and wash beans; place in a large Dutch oven. Cover with water to 2 inches above beans; bring to a boil, and cook 2 minutes. Remove from heat; cover and let stand 1 hour. Drain beans; place in Dutch oven. Cover with water to 2 inches above beans; bring to a boil. Reduce heat, and simmer 1 hour or until tender. Drain.
Cook bacon in the Dutch oven over medium-high heat until crisp. Remove bacon from Dutch oven, reserving 2 teaspoons drippings in Dutch oven. Crumble bacon. Heat drippings over medium-high heat. Add garlic; sauté 2 minutes or until golden. Stir in beans and bacon; remove from heat.
Divide beans evenly among 6 plates; arrange lamb on beans. Spoon sauce over lamb. Garnish with rosemary sprigs, if desired.