1. Combine 1 tablespoon lime juice, 2 teaspoons oil, cumin, 1/8 teaspoon salt, red pepper, and 1 cup beans in a food processor; process until smooth, scraping sides of bowl as needed.
2. Place remaining 1 1/2 teaspoons lime juice, remaining 2 teaspoons olive oil, remaining 1/8 teaspoon salt, remaining beans, tomato, bell pepper, cucumber, red onion, cilantro, and jalapeño in a bowl; toss well to combine.
3. Spread about 3 1/2 tablespoons processed bean mixture inside each pita half. Place 1 lettuce leaf, about 3/4 cup tomato mixture, and 2 tablespoons cheese inside each pita half. Serve with lime wedges.