Preheat oven to 350 degrees F.
Trim most of the fat from the lamb and season with salt and pepper. In a heavy bottomed Dutch oven (at least 6 quarts), heat olive oil until smoking. Brown lamb on both sides until dark golden brown and remove. Add onions, garlic, anchovies and orange pieces and cook until softened, scraping the casserole bottom with a wooden spoon to loosen the brown bits. Add olives, orange juice, wine and tomato sauce and bring to a boil. Add lamb, lower heat to a simmer and cook 70 minutes, or until fork tender.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. The sauce may be refrigerated for up to one week or frozen for up to 6 months.