In a large heavy skillet, heat 1 tablespoon oil over medium heat. Add the chopped onion and cook until lightly browned, about 8 minutes; transfer to a medium bowl. Wipe out the skillet and reserve.
Using a food processor, puree 1 cup chickpeas with 1/4 cup of the reserved chickpea liquid, the lemon peel, lemon juice and half of the parsley; season with salt and pepper. Transfer to a small bowl and cover. Add the lamb, the cooked onions, 1 1/2 tablespoons flour, 1 teaspoon salt and the remaining chickpeas and parsley to the food processor and pulse until the chickpeas are coarsely chopped. Divide the mixture evenly into 8 patties.
Preheat a grill pan over medium-high heat. Brush the zucchini with 2 tablespoons oil and season with salt and pepper. Grill the zucchini, turning once, until crisp-tender, 3 to 4 minutes; transfer to a plate. Add the flatbreads to the grill and heat on both sides; wrap in foil to keep warm.
Add the remaining 2 1/2 tablespoons flour in a shallow bowl. In the reserved skillet, heat the remaining 1 cup plus 5 tablespoons oil over high heat. Coat the patties with flour; add to the skillet and fry until crisp and browned, 1 to 2 minutes on each side. Transfer to paper towels to drain.
Spread the chickpea sauce on the inside of each flatbread. Divide the zucchini and lamb patties among the flatbreads and add the sliced onions. Lay each sandwich on a piece of foil, wrap each into a cone shape and serve immediately.