Bring the lima beans and 1 inch of water to a boil in a saucepan. Reduce the heat and simmer, covered, until tender, 5 minutes for frozen beans. Drain and set aside.
While the lima beans are simmering, put the 4 cups of corn and 2 inches of water in a saucepan and bring to a boil. Reduce the heat and simmer, covered, until tender, 3 to 5 minutes.
Drain well and roast the corn in a large, dry cast iron skillet, stirring occasionally, until golden brown, about 3 minutes. Stir in the lima beans, chives, tarragon, butter, salt and pepper. Cook until the flavors are blended, about 5 minutes. Serve at once.