Preheat oven to 325 degrees. Cut 1 pound of the potatoes into 1/4-inch-thick rounds; spread them out in a large (5- to 6-quart) heavy-bottom pot or Dutch oven. Layer half the onions on top of the potatoes.
Place lamb cubes on top of onions. Sprinkle with 1 1/2 teaspoons salt; season with pepper. Add the thyme. Place remaining onions on top of lamb. Add the stock and 1 cup water.
Place whole potatoes on top of onions. Sprinkle with remaining teaspoon salt; season with pepper. Cover with a tight-fitting lid; bring to a boil over medium-high heat. Transfer to oven; cook, without stirring, 2 hours. Sprinkle with parsley.