Heat 2 inches of water to boil in 4-quart Dutch oven. Add potatoes, green beans and 1/2 teaspoon salt. Heat to boiling and reduce heat to medium. Cover and cook about 10-15 minutes or until vegetables are tender. Drain and set aside.
While vegetables are cooking, melt butter in 12-inch skillet over medium-high heat. Cook onions in butter 10 to 12 minutes, stirring occasionally, until golden brown.
Stir in vinegar, brown sugar and 1/4 teaspoon salt. Pour onion mixture over potatoes and green beans and stir until coated.
Arrange lettuce on large platter. Arrange warm vegetables on lettuce. Sprinkle with pepper.