Trim and reserve fat and bones from lamb. Cut meat into 1 1/2-inch pieces. Place fat in heavy large Dutch oven over medium-high heat. Cook fat until 3 tablespoons drippings are rendered, about 5 minutes. Using large spoon, remove any solid fat from pot; discard. Sprinkle lamb with salt and pepper. Working in batches, add lamb to pot; saute until brown on all sides, about 5 minutes per batch. Using slotted spoon, transfer lamb to plate. Add bones to pot; cook until brown, about 5 minutes. Using tongs, transfer bones to plate.
Add vegetables, parsley and thyme to pot; stir to coat with drippings. Return meat and bones to pot. Add 2 cups water and bring to boil. Reduce heat to medium-low. Cover pot tightly; simmer until lamb is tender and vegetables are soft, stirring occasionally, about 1 1/2 hours.
Discard bones. Place 1 cup vegetables in processor; puree. Add to stew. Season with salt and pepper. (Can be made 1 day ahead. Cover; chill. Simmer before serving.)