Drain tuna, drain and rinse chickpeas, halve cherry tomatoes, and dice onion. Rinse lettuce leaves and pat dry; rinse and peel carrots, then cut into sticks.
In a mixing bowl blend together yogurt, Parmesan cheese, lemon juice, and chopped dill (optional). Add tuna, chickpeas, tomatoes, and onions; toss to coat evenly. Divide tuna salad evenly among lettuce leaves and wrap up.