Place eggplant into a colander set in a bowl or the sink; sprinkle with 1 teaspoon salt and toss to coat. Let eggplant stand for at least 1 hour. Rinse off the bitter liquid and excess salt and drain well.

Heat 1 tablespoon olive oil in a large skillet over medium heat. Stir in onion and celery; cook and stir until onion has softened and turned translucent and celery is fragrant, about 5 minutes.

Combine cumin, oregano, rosemary, paprika, mint, salt, and black pepper in a small bowl or mortar and pestle and mix to make the lamb seasoning. Set aside.

Stir eggplant cubes and garlic into vegetables in the skillet. Cook for 5 minutes more. Add tomatoes and sprinkle with 1/2 of the lamb seasoning. Stir gently and cook for another 5 minutes.

Preheat the oven to 375 degrees F (190 degrees C). Grease a 2-quart casserole dish.

Pour 1/2 of the tomato sauce and chicken broth into the skillet and simmer for 10 minutes; add water if sauce starts drying up. Transfer the sauce to the casserole dish.

Heat the remaining olive oil in the skillet over medium-high heat. Cook ground lamb with the remaining seasoning mixture until browned, forming imperfect meatballs.

Transfer lamb to the casserole dish, partially submerging it in vegetable mixture. Combine lemon juice with the remaining tomato sauce and pour it over the casserole.