For the chickpeas: Preheat the oven to 425 degrees F. Combine the chickpeas, olive oil, cumin, coriander, paprika, cayenne pepper, cinnamon and a pinch each of salt and pepper in a large bowl. Toss to coat.
Spread on a rimmed baking sheet and roast until browned and slightly crispy, 25 to 30 minutes.
Wrap the pitas in foil and place in the oven for the last 2 minutes of cooking to warm.
For the hummus-dill dressing: Meanwhile, whisk together the hummus, lemon juice, dill and garlic. Thin with water, if needed, for desired consistency.
For serving: Divide the cucumber, lettuce, tomato and red onion among the pitas and top with chickpeas. Drizzle with hummus dressing, wrap pitas around the filling and serve.