Heat oven to 400 degrees with rack in center. Place a baking sheet on rack below to catch any drips from gratin. Brush a 10-by-5 1/2-inch gratin dish with melted butter.
Cover bottom of gratin dish with one-third of potato slices in an even layer. Sprinkle potatoes with one-third each of thyme, nutmeg, and lemon zest; season with salt and pepper. Dot with butter. Add a second layer, and season. Top with a third layer of neatly arranged potato slices. Pour milk over potatoes. Sprinkle with remaining third thyme, nutmeg, and lemon zest, and dot with butter. Season to taste with salt and pepper. Cover with aluminum foil.
Bake for 40 minutes. Remove foil, and continue to bake 10 to 20 minutes, until top is golden brown and potatoes are tender when pierced with the tip of a knife. If the top of the gratin is not golden brown but potatoes are tender, heat the broiler. Place gratin under the broiler for just a few seconds to brown nicely. Serve gratin hot, spooned out into individual servings. Potato gratin will hold well in a low oven (about 200 degrees, covered with aluminum foil for up to 1 hour).