Preheat oven to 400°F and slice eggplant into 1/2-inch rounds.
Arrange eggplant on a baking sheet, spray lightly with oil, and roast for 15-20 minutes until tender.
In a skillet over medium heat, sauté diced onion and minced garlic in olive oil until translucent.
Add ground lamb to the skillet, browning it while breaking it into crumbles.
Stir in tomato puree, cinnamon, oregano, salt, and pepper; simmer for 5 minutes until thickened.
In a small bowl, whisk together Greek yogurt, egg, and parmesan cheese until smooth.
In a small oven-safe dish, layer half the eggplant, followed by the lamb mixture, and the remaining eggplant.
Spread the yogurt mixture evenly over the top and bake at 375°F for 20 minutes until the topping is set and golden.