Melt the sugar in a heavy-bottomed saucepan over medium heat, washing down the sides with a wet pastry brush, until deep amber, 8 to 10 minutes. Add lemon juice, whisk in the butter, then slowly whisk in the cream and stir in the salt. Cool completely.
Preheat oven to 350 degrees F. Grease and flour three cake pans and line the bottoms with parchment rounds.
Whisk the cake flour, baking powder, baking soda, cinnamon, nutmeg, and salt in a medium bowl.
In a stand mixer, beat the butter, oil, and both sugars on medium speed for 3 minutes until light and fluffy.
Add eggs one at a time, mixing until just combined after each.
Mix in the vanilla extract.
With the mixer on low, add the flour mixture in three additions, alternating with the buttermilk in two additions, starting and ending with flour.
Gently fold in the diced apples by hand.
Divide the batter among the three pans and bake for 26 to 30 minutes, until a toothpick comes out clean.
Cool in the pans for 10 minutes, then transfer to a wire rack to cool completely before frosting.
Beat the butter until creamy, add powdered sugar gradually, then mix in 1/4 cup of the caramel sauce and salt until fluffy.
Frost between each layer, apply a thin crumb coat, refrigerate for 20 minutes, then apply the final coat of frosting and drizzle with the remaining caramel.
Slice and serve, or refrigerate until ready to serve.