To prepare lamb mixture, cook lamb in a large Dutch oven over medium-high heat until browned; stir to crumble. Remove from pan; drain. Set aside. Wipe skillet with paper towels.
Add onion to pan coated with cooking spray; sauté 5 minutes. Add lamb, currants, and next 7 ingredients (currants through garlic); bring to a boil. Cook until thick (about 30 minutes).
To prepare sauce, cook 1 1/2 cups milk and butter in a heavy saucepan over medium-high heat to 180° or until tiny bubbles form around edge (do not boil). Remove from heat. Combine 1/2 cup milk, egg whites, flour, and 1/2 teaspoon salt in a large bowl; gradually add the hot milk mixture to the egg white mixture, stirring constantly with a whisk. Return milk mixture to pan, and cook until thick (about 15 minutes), stirring constantly. Remove from heat.
Place half of eggplant slices on a baking sheet coated with cooking spray, and brush with 1 1/2 teaspoons oil. Broil 4 minutes on each side or until browned. Repeat procedure with remaining eggplant and 1 1/2 teaspoons oil.
Preheat oven to 375°.
Cook potato slices in boiling water 5 minutes or until crisp-tender; drain. Rinse with cold water; drain well.
Arrange potatoes in the bottom of a 13 x 9-inch baking dish coated with cooking spray. Arrange half the eggplant slices over potatoes. Pour 4 cups lamb mixture over eggplant, and sprinkle with 1 tablespoon cheese. Arrange remaining eggplant over cheese, and top with the remaining lamb mixture. Sprinkle with 1 tablespoon cheese. Spread sauce over cheese, and sprinkle with 2 tablespoons cheese. Bake at 375° for 45 minutes or until top is golden brown. Let stand 15 minutes. Garnish with oregano sprigs, if desired.