1. To prepare sauce, combine the first 4 ingredients; set aside.
2. To prepare falafel, drain chickpeas in a colander over a bowl; reserve liquid. Place chickpeas, 3 tablespoons liquid (discard remaining liquid), breadcrumbs, and next 5 ingredients (through cumin) in a food processor; process until minced. Divide chickpea mixture into 8 equal portions, shaping each into a 1/2-inch-thick patty.
3. Heat oil in a large nonstick skillet over medium-high heat. Add patties to pan; cook 3 minutes on each side or until golden brown. Spread about 1/4 cup sauce into each pita half. Fill each pita half with 1/2 cup lettuce, 1/4 cup tomato, about 2 tablespoons sliced cucumber, 1 tablespoon sliced onion, and 2 patties.