1. Rinse and drain lentils; place lentils and rice in a large saucepan. Cover with water to 3 inches above lentil mixture; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until lentils and rice are tender. Drain.
2. Place lentil mixture in a food processor; pulse until finely chopped. Set aside (keep mixture in processor).
3. Heat a large skillet over medium heat. Add 1 tablespoon oil to pan; swirl to coat. Add green onions to pan; cook 2 minutes or until softened. Stir in tomato paste and red pepper; cook 1 minute, stirring frequently. Add green onion mixture, 2 tablespoons cilantro, lemon juice, and salt to food processor; process until combined.
4. Divide mixture into 12 equal portions, gently shaping each into a 1/2-inch-thick patty. Return skillet to medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add 6 patties to pan; cook 3 minutes on each side or until browned. Remove cooked patties from pan. Repeat procedure with remaining 1 tablespoon oil and 6 patties. Sprinkle with remaining 2 tablespoons cilantro. Serve patties with cucumber and lemon wedges.