For the Eggplant and Potatoes: Season the eggplant and potatoes with salt and pepper. Add 1/2 inch of oil to a large skillet and heat. When the oil is hot, fry the potato slices, flipping once, until golden brown, about 3 to 4 minutes per side. Remove the potatoes to a paper towel lined plate. Replenish the oil so there is still 1/2 inch in the bottom of the pan. Fry the eggplant slices in the oil, flipping once, until golden brown, about 3 minutes per side. Add more oil as necessary. Remove the eggplant from the pan and place on a paper towel lined plate.
For the Lamb Tomato Sauce mixture: Place a saute pan on the stove over medium high heat. When the pan is hot, add the ground lamb. Saute the ground lamb for 2 minutes, until it begins to turn brown. Add the onions and garlic and saute for 5 more minutes. Season with salt and pepper. Drain off any excess fat from the pan. Season the mixture with oregano, bay leaf, cloves and cinnamon and cook for 3 more minutes. Deglaze the pan with red wine. Cook over medium high heat until the red wine has reduced by half, about 10 minutes. Add the tomatoes. Cook, stirring occasionally until the mixture is a thick tomato sauce consistency, about 30 minutes. Check for seasoning. Remove from the heat and cool completely.
For the Bechamel: In a saucepan, melt the butter. Add the flour to make a roux. Cook the roux over medium heat for 3 or 4 minutes, or until it becomes a very pale tan color. Slowly add the milk, whisking constantly. Add the nutmeg and the lemon juice. Simmer, stirring constantly, over low heat for 15 minutes. The mixture should be fairly thick. In a separate bowl, whisk the eggs together. Take 1/2 cup of the hot milk mixture and whisk it into the beaten eggs. This will temper the eggs. Whisk the egg/milk mixture back into the milk mixture. Add the Parmesan cheese and stir. Over very low heat, cook this mixture for 3 more minutes. Be careful not to let the mixture simmer. Season with salt and pepper. Remove from the heat and cool.
To finish: Preheat the oven to 350 degrees. Sprinkle the bottom of a 9x13 inch-baking dish with 1/4 cup of breadcrumbs. Place a layer of the eggplant over the breadcrumbs. Place a layer of the potatoes over the eggplant. Place 1/2 of the lamb tomato sauce mixture over the potatoes. Spread 1/3 of the bechamel sauce over the lamb mixture. Top the bechamel with another layer of eggplant and another layer of potatoes. Top with the remaining lamb mixture. Place one more layer of eggplant and potatoes over the lamb mixture. Top with the remaining bechamel. Sprinkle with the remaining breadcrumbs and the Parmesan cheese. Place in the oven and bake for 45 minutes, or until the top is golden brown. Remove from the oven and let sit for 10 minutes before serving. Sprinkle with mint and parsley.