In a medium bowl combine egg product, 1 teaspoon of the oil, and the oregano. Add the crushed crackers, zucchini, carrots, and green onions to egg mixture; mix well. Shape the vegetable mixture into four 3 1/2-inch patties.
In a large nonstick skillet heat the remaining 2 teaspoons oil over medium heat. Cook the patties in hot oil for 5 to 7 minutes or until golden brown, turning once. Meanwhile, for sauce, in a small bowl combine the yogurt, garlic, and lemon peel.
Serve patties in pita bread halves with the lettuce, tomato, cucumber, and sauce.