Preheat the oven to 350 degrees F. Melt the butter in a large pot. Stir in the brown sugar and 1/2 cup water. Bring to a boil, then reduce the heat to medium and simmer, stirring, until reduced and thickened, about 10 minutes.
Bring a large pot of water to a boil. Meanwhile, peel the potatoes and cut them lengthwise, then lengthwise again, making long quarters. Cut the quarters into 1-inch pieces. Boil the potatoes until they give a bit when poked with a fork, about 5 minutes.
Drain the potatoes and arrange in a single layer in a buttered 3-quart baking dish. Pour the syrup on top, making sure it covers the potatoes. Place the lemon slices on top and bake 35 minutes, spooning the syrup over the potatoes twice during that time. The potatoes are done when they are fork-tender.
Remove from the oven, discard the lemon slices and stir in the pecans. Top with the marshmallows. Turn the oven up to 400 degrees F, place the baking dish back in the oven, and cook until the marshmallows puff and turn brown, about 10 more minutes.