Pare the eggplant and cut crosswise into 1/4-inch slices. Sprinkle slices with 1 teaspoon salt. Coat with 1/2 cup flour; shake off excess. Fry several eggplant slices in hot oil until golden brown. Repeat with remaining slices, adding more oil when necessary; drain on paper towels.
Melt 2 tablespoons butter or margarine in 10-inch skillet. Cook lamb and onion in butter over medium heat until lamb is brown. Stir in tomato sauce, wine, 1/2 teaspoon salt, pepper and 1/4 teaspoon nutmeg. Cook uncovered until half of the liquid is absorbed, about 20 minutes. Stir in 1 beaten egg, 1/4 cup parmesan cheese and 1/4 cup bread crumbs. Remove from heat.
Melt 3 tablespoons butter in 2-quart saucepan. Stir in 3 tablespoons flour, 1/2 teaspoon salt and 1/4 teaspoon nutmeg. Cook over low heat, stirring constantly, until mixture is smooth and bubbly. Add milk, stirring constantly until sauce boils.
Beat 2 eggs slightly. Stir small amount of hot milk mixture into eggs to temper them. Stir egg-milk mixture back into hot mixture in pan. Add 1/4 cup parmesan cheese.
Grease a 12 x 8 x 2 inch baking dish. Sprinkle 1/4 cup bread crumbs evenly in dish. Arrange half of the eggplant slices in dish; cover with lamb mixture. Sprinkle with 2 tablespoons of the cheese; top with remaining eggplant slices. Pour sauce over eggplant slices; sprinkle with remaining parmesan cheese. Bake uncovered 45 minutes.
Remove from oven; let stand 20 minutes before serving.