Trim fat from lamb, and cut lamb into 1-inch cubes.
Combine lamb, sliced leek, barley, peas, and broth in a large Dutch oven, and bring to a boil. Reduce heat, and simmer 45 minutes, stirring occasionally.
Add the turnips and remaining ingredients, and bring to a boil. Reduce heat, and simmer 40 minutes or until turnips are tender.