Cut zucchini crosswise into 1-inch-thick slices. In a large saucepan cover potatoes with salted cold water by 2 inches and simmer, covered, until tender, about 35 minutes. Transfer potatoes to a colander and reserve cooking water. When potatoes are cool enough to handle, peel and put in a large bowl. Add lemon thyme, butter, and salt and pepper to taste and with a potato masher coarsely mash. Keep mash warm, covered.
Bring cooking water to a boil and simmer zucchini until tender, about 8 minutes. Drain zucchini well in colander and coarsely mash into potatoes. Mash may be made 1 day ahead and cooled completely before being chilled, covered. Reheat mash before serving.
