Marinate the chicken: In a bowl, combine chicken, cumin, coriander, paprika, 1 tsp salt, black pepper, yoghurt, 3 grated garlic cloves, and the juice of one lemon. Mix well. Refrigerate for 2-24 hours.
Cook the chicken: Light the charcoal. Skewer the marinated chicken and place it on the spit to cook. Grill until it's nicely coloured on the outside and cooked through, approximately 45 minutes. Shave off the cooked outer layer, allowing the layer underneath to get some colour before shaving more.
Prepare the Toum (garlic sauce): In a blender, combine the remaining garlic cloves with a pinch of salt and the juice of the remaining lemons. Blend for 1 minute. Gradually stream in the oil to emulsify into a smooth sauce.
Assemble and serve: Heat the flatbread over the grill. Spread some Toum on the bread, then add chicken, lettuce, tomato, and onion. Roll it up tightly and enjoy!