Rinse and pat dry eggplants, trim the ends and cut into 1 cm slices lengthwise (approximately 1/2 inch). Arrange next to each other on a plate and season with salt on both sides, let stand for about 30 minutes.
Peel and halve an onion, dice finely. Rinse and dice tomatoes. Heat 5 tablespoons of oil in a pan and saute tomatoes, bell pepper and onion for a few minutes, season with sugar, salt and pepper and simmer for about 10 minutes on low heat. Add parsley and remove from heat, cool.
Pat dry eggplant slices. Heat 5 tablespoons of oil in a pan and cook eggplant slices until lightly browned on both sides. Drain on paper towels.
Butter large baking dish with 1 teaspoon of butter. Heat remaining butter in a saucepan and saute flour for a few minutes, gradually add milk, stirring constantly, and bring to a boil. Season with salt, pepper and lemon zest to taste, remove from heat. Grate Parmesan and mix with eggs, whisk into slightly cooled sauce.
Line baking pan with half of eggplant slices. Top with lamb steaks, season with pepper and sprinkle with onion and tomato mixture. Spread with remaining eggplant slices and pour cheese sauce over. Bake in preheated oven at 160°C (approximately 325°F) for about 1 hour. Remove from the oven and serve hot.