Add lamb and cook until browned on all sides, 6 minutes. Remove from pan and set aside. Reduce heat to medium.
Add onion, carrots, celery, and garlic to casserole; cook until golden, about 10 minutes. Increase heat to high. Add red wine and vinegar. Bring to a boil over medium-high heat and cook until reduced by two thirds, about 5 minutes.
Add broth and lamb to casserole; bring to a boil, then reduce to simmer (2 to 3 minutes). Meanwhile, tie together bay leaf, rosemary, and thyme with kitchen string; add to casserole. Cover and bake 1 to 1 1/4 hours, or until lamb is tender.
Remove lamb from casserole. Strain out vegetables and discard them, saving the liquid. Return liquid to casserole, bring to a boil over medium-high heat, and cook until reduced to 1 to 1 1/2 cups, about 20 minutes.
Return lamb to the reduced braising liquid and keep warm until serving. To serve, spoon sauce over lamb.