Preheat oven to 400°F and line a baking sheet with parchment paper.
Arrange eggplant and potato slices on the sheet, brush with olive oil, and roast for 15 minutes until tender.
In a skillet over medium heat, sauté the onion, garlic, and ground lamb until the meat is browned.
Stir in the tomato puree, cinnamon, sea salt, and black pepper, then simmer for 5 minutes.
In a small bowl, whisk together the Greek yogurt and egg until smooth.
In a small oven-safe dish, layer the potatoes, then the eggplant, followed by the lamb mixture.
Pour the yogurt custard over the top and bake for 20 minutes until the topping is set and lightly browned.