Sprinkle eggplant slices with salt and set aside for 30 minutes. Rinse and pat dry.
Preheat oven to 190 degrees C.
Heat oil in a large frypan over medium-high heat. Lightly brown eggplant and zucchini slices on both sides; drain. Add more oil if necessary, brown potato slices; drain.
Saute onion and garlic until lightly browned. Pour in vinegar and reduce. Stir in tomatoes, lentils, 1/2 the juice from lentils, oregano and parsley. Cover, reduce heat to medium-low, and simmer 15 minutes.
In a 23x33cm casserole dish layer the eggplant, zucchini, potatoes, onions and feta. Pour tomato mixture over vegetables; repeat layering, finishing with a layer of eggplant and zucchini.
Cover and bake in preheated oven for 25 minutes.
Meanwhile, in a small saucepan combine butter, flour and milk. Bring to a slow boil, whisking constantly until thick and smooth. Season with pepper and add nutmeg. Remove from heat, cool for 5 minutes, and stir in beaten egg.
Pour sauce over vegetables and sprinkle with Parmesan cheese. Bake, uncovered, for another 25 to 30 minutes.