Combine eggs and water in a large bowl, stirring with a fork. Stir in oats and next 5 ingredients. Shape mixture into 4 patties.
Pour oil into a large nonstick skillet, and cook over medium-high heat until hot. Add patties, and cook 3 minutes on each side or until lightly browned. Add 1/2 cup water; cover, reduce heat, and simmer 10 minutes or until water evaporates. Serve patties on buns with lettuce, tomato slices, and mayonnaise or salad dressing.