Preheat your oven to 400°F (200°C). Brush the eggplant slices with olive oil on both sides and season with salt and pepper. Arrange them in a single layer on a baking sheet and bake for 25 minutes, flipping halfway through, until golden and soft.
Meanwhile, in a saucepan, add lentils and cover with water. Bring to a boil, reduce heat, and simmer for 20-25 minutes until tender. Drain and set aside.
In a large skillet over medium heat, sauté the onion in 2 tablespoons of olive oil until translucent. Add the garlic, oregano, cinnamon, and nutmeg, cooking for 1 minute until fragrant.
Stir in the cooked lentils and crushed tomatoes. Simmer for 10 minutes, allowing flavors to meld. Season with salt and pepper to taste. Remove from heat.
For the béchamel sauce, melt butter in a saucepan over medium heat. Whisk in flour and cook for 2 minutes. Gradually add milk, whisking continuously to prevent lumps. Cook until the sauce thickens, about 5 minutes. Remove from heat, stir in the beaten egg and Parmesan cheese, and season with salt and nutmeg.
To assemble the moussaka, spread half of the lentil mixture in a greased 9x13-inch (23x33 cm) baking dish. Layer with half of the eggplant slices. Repeat with the remaining lentil mixture and eggplant slices.
Pour the béchamel sauce over the top layer of eggplant, spreading to cover.
Bake for 30 minutes, or until the top is golden and the sauce is bubbly.
Allow the moussaka to rest for 10 minutes before serving.