Vegetarian Moussaka

Name: Vegetarian Moussaka
Ingredients: 1 eggplant, thinly sliced; 1 teaspoon salt, or more as needed; 1 tablespoon olive oil, or more as needed; 1 large zucchini, thinly sliced; 2 potatoes, thinly sliced; 1 onion, sliced; 1 clove garlic, chopped; 1 tablespoon white vinegar; 1 (14.5 ounce) can whole peeled tomatoes, chopped; 0.5 (14.5 ounce) can lentils, drained with liquid reserved; 2 tablespoons chopped fresh parsley; 1 teaspoon dried oregano; ground black pepper to taste; 1 cup crumbled feta cheese; 1.25 cups milk; 2 tablespoons all-purpose flour; 1.5 tablespoons butter; 1 pinch ground nutmeg; 1 large egg, beaten; 0.25 cup grated Parmesan cheese