Bring stock to boil in heavy medium saucepan. Remove from heat. Add ancho chilies. Cover and let stand until soft, about 30 minutes. Transfer ancho chilies and 2 cups stock to processor. Add chipotle chilies and puree. Strain if necessary to remove large pieces of chili skin. Stir puree into remaining stock. Set stock mixture aside.
Heat 1/4 cup olive oil in large Dutch oven over high heat. Add lamb meat and reserved bones in batches and cook until meat is brown, about 3 minutes per batch. Transfer to bowl using slotted spoon. Add remaining 2 tablespoons oil to Dutch oven. Add onions and garlic and saute 3 minutes. Return meat, bones and juices accumulated in bowl to Dutch oven. Add beer and simmer 10 minutes. Add stock mixture, tomatoes, chili powder and cumin and simmer until lamb is tender, about 1 hour 10 minutes.
Mix beans and lime juice into chili. Season with salt and pepper. (Can be prepared 1 day ahead. Cover and refrigerate). Simmer chili until heated through. Discard lamb bones. Serve passing Avocado Salsa, sour cream and cilantro separately.