For the cornbread: Preheat the oven to 400 degrees F.
Meanwhile, put the butter in a 10-inch cast-iron skillet and leave in the oven until melted, about 8 minutes. Carefully remove from the oven and set aside.
Mix the cornmeal, flour, baking powder and a generous pinch of salt and pepper in a medium bowl until combined. Whisk together the sweet potato puree, milk, honey, eggs and lemon juice in a large bowl. Pour the melted butter into the wet ingredients and whisk to combine. Stir the dry ingredients into the wet ingredients, then pour the batter into the cast-iron skillet.
Lower the oven to 350 degrees F. Bake the cornbread until golden orange and a toothpick inserted in the center comes out clean, 35 to 40 minutes. Cool completely, then cut into 1/2-inch cubes.
Line a baking sheet with parchment and spread the cornbread cubes on top. Toast in the oven, flipping halfway through, until browned and crispy along the edges, about 20 minutes. Set aside. (Leave the oven on.)
For the dressing: Crumble the sausage into a large skillet. Cook over medium heat, stirring frequently, until browned, about 8 minutes. Remove the sausage crumbles from the pan with a slotted spoon and remove to a large bowl. Add the onion, celery, carrot and thyme to the skillet with the sausage fat, then sprinkle with salt and pepper. Sweat the vegetables, stirring occasionally, until softened, about 10 minutes. Add to the bowl with the sausage, then add the chicken stock, apple cider and cornbread cubes and stir until moist but not mushy. Place in a 9-inch square casserole dish and bake until the top is crusty and golden, about 30 minutes.