Preheat oven to 400F. Immerse sliced eggplant in a large bowl of heavily salted water and soak for 10-15 minutes. Drain and blot dry. Dip each eggplant slice in beaten egg, and then in bread crumbs to coat. Pour olive oil into a heavy skillet to a depth of 1 inch and heat over medium-high heat. Fry the eggplant until golden brown, turning once, about 1-2 minutes per side. Transfer to a plate lined with paper towel to drain. In a heavy skillet, heat about 2 tbsp of oil that the eggplant was fried in over high heat. Season the lamb chops on both sides with salt and pepper. Sear the lamb chops on both sides until browned. Lay the lamb chops in the bottom of a small baking dish. Cover the chops with onion, tomato and pepper slices. Season with salt and pepper. Top casserole with eggplant. Sprinkle with Parmesan cheese if desired. Bake for 3-35 minutes, until lamb is cooked through and vegetables are cooked. Serves 2 or 3.