Heat oil in a large pot over high heat. Add lamb; cook and stir until browned, 3 to 5 minutes. Reduce heat to medium; add potatoes, tomatoes, zucchini, onions, chickpeas, and carrots. Stir in celery, mint, cilantro, ginger, cinnamon, and saffron. Cover with water and simmer for 15 minutes.
Reduce heat to low. Stir in tomato puree and enough water to cover. Simmer, adding more water as it is absorbed, until chickpeas are tender, about 45 minutes. Transfer lamb to a plate using a slotted spoon.
Puree chickpea mixture with an immersion blender until smooth. Season with salt and pepper. Season lamb with salt and pepper; stir back into the pot.
