In a medium saucepan bring the 1 1/4 cups water to boiling; stir in quinoa. Return to boiling; reduce heat. Simmer, covered, for 8 minutes. Stir in corn. Return to boiling; reduce heat. Simmer, covered, for 5 minutes more. Remove from heat. Let stand, covered, for 10 minutes.
In a large bowl combine eggs, cornmeal, chopped red onion, parsley, cilantro, oregano, garlic, 1/2 teaspoon of the salt, and the cayenne pepper. Stir in quinoa mixture and bread crumbs.
Using about 1/3 cup mixture for each patty, shape quinoa mixture into eight 3/4-inch-thick patties. Heat a lightly greased griddle over medium heat. Cook patties, half at a time, on hot griddle for 6 to 8 minutes or until heated through and golden, turning once. Keep patties warm in a 300°F oven while cooking the remaining patties.
Meanwhile, in a large bowl whisk together vinegar, oil, black pepper, and the remaining 1/4 teaspoon salt. Add lettuce, tomato, and sliced red onion; toss gently to coat. Divide lettuce mixture among serving plates. Top each serving with two cooked patties.