Preheat the oven to 375 degrees . Brush the apples with the lemon juice. Grease a small baking dish and add 2 tablespoons water. Place the apples cut side down in the dish and bake until tender, 20 minutes.
Microwave the sweet potato at high power for 5 minutes; peel. In a saucepan, boil the squash and enough water to cover until the squash softens, about 15 minutes; strain. Mash together the sweet potato, squash, brown sugar, cinnamon, cloves and nutmeg.
Using a melon baller, scoop the flesh from each apple into a medium bowl, leaving a 1/4-inch-thick shell. Using a handheld mixer, combine the apple flesh with the squash mixture, heavy cream and butter.
Place the apple shells on a baking sheet, fill with the squash mixture and broil for 3 minutes. Top with whipped cream.