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.

Meanwhile, combine cumin, oregano, rosemary, paprika, mint, salt, and black pepper in a small bowl or mortar and pestle and mix well; this is the lamb seasoning (see Cook’s Note). Set seasoning aside.

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

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 a little water if sauce starts to get dry. Transfer sauce to the prepared casserole dish.

Return the skillet to the stove over medium-high heat and add remaining 1 tablespoon olive oil. Place ground lamb into the skillet and sprinkle with remaining seasoning mixture. Cook lamb in hot oil, stirring frequently, until evenly browned; it should look like imperfect meatballs.

Gently transfer lamb to the casserole dish, pushing it down into vegetable mixture so that it is at least partially submerged. Stir lemon juice into remaining tomato sauce and pour sauce over casserole.

Bake uncovered in the preheated oven for 45 to 60 minutes, depending on how tender you like your vegetables.