Heat oven to 425 degrees. Bake potatoes until soft, 40 to 45 minutes. When cool enough to handle, peel and place flesh in a medium bowl; add salt, and mash with a fork.
Meanwhile, slice apples into 1/8-inch-thick wedges and place in a medium bowl. Add lemon juice and toss to combine.
In a medium skillet, melt 3 tablespoons butter over medium-high heat. Add 2 tablespoons brown sugar and cook, stirring, until sugar dissolves. Cook apple slices in the butter and sugar in 3 or 4 batches, until golden and caramelized, about 1 minute on each side. As they finish cooking, transfer to a plate and set aside.
In a medium skillet, melt 3 tablespoons butter over high heat. Add 2 tablespoons brown sugar and cook until sugar dissolves. Stir in 4 tablespoons cream and the Calvados and cook until slightly thickened, about 1 minute. Remove from heat and add to sweet potatoes, mixing well to combine. Transfer potato mixture to a buttered 3-quart ovenproof casserole. Arrange apple slices over potatoes; set aside.
In a medium skillet, melt remaining 3 tablespoons butter over medium heat. Add remaining 2 tablespoons brown sugar and cook until dissolved. Add remaining 2 tablespoons of cream and cook, stirring, for 30 seconds. Stir in orange juice and cook for 1 to 2 minutes, until thickened and dark brown. Pour over the apples and cover with aluminum foil.
Bake until heated through, about 30 minutes. Remove from oven and serve immediately, or let stand at room temperature for up to 30 minutes before serving.