For the Cheesecake Layer
Preheat oven to 325 degrees. Set a kettle of water to boil. Using an electric mixer, beat cream cheese on medium until fluffy, scraping down side of bowl. Gradually add sugar, beating until fluffy. Beat in lemon zest and juice, and salt. Beat in vanilla and eggs, one at a time, scraping down side of bowl after each addition. Beat in sour cream.
Cut parchment paper in a circle and line the bottom of the cheesecake pan. Wrap bottom half of pan in foil. Pour in filling; place in a roasting pan or an oven safe dish. Pour in boiling water to come halfway up side of springform. Bake until just set in center, about 45 minutes. Use a toothpick to check the center if needed. Remove pan from water; let cool 20 minutes. Run a paring knife around edge; let cool completely. Cover; chill overnight, then wrap in plastic wrap and freeze.
For the Carrot Cake Layers
Heat oven to 350 degrees.
Spray two 9" round pans with nonstick baking spray. Sprinkle pans with flour and shake to distribute evenly.
Place the raisins in a small saucepan, cover with boiling water, cover the pan, & let soak for 20 minutes until nice & plump. Drain well & let stand on a paper towel. Finely chop the walnuts and roast in a frying pan on medium heat for a few minutes.
Combine the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt in large bowl and whisk together; set aside.
Using a cheese grater, shred carrots using large holes of box grater; move carrots to bowl and set aside.
In bowl of standing mixer fitted with paddle attachment, beat granulated and brown sugars, vanilla and eggs on medium-high until thoroughly combined, about 45 seconds.
Reduce speed to medium. Drizzle oil in slow, steady stream using the side of the bowl to direct the oil in.
Increase speed to high and mix until mixture is light in color and well emulsified, about 45 seconds to 1 minute longer.
Turn off mixer and stir in carrots, walnuts or pecans, raisins and dry ingredients by hand until incorporated and no streaks of flour remain.
Pour into prepared pan and bake until toothpick or skewer inserted into center
Pineapple Cream Cheese Frosting
When cake is cold, prepare the frosting. In a bowl of an electric mixer, combine cream cheese, butter, powdered sugar, teaspoon vanilla, reserved pineapple juice and a dash of salt. Beat until smooth and of spreading consistency.
To Assemble the Cake
Place bottom layer of carrot cake on cake stand.
Unwrap cheesecake layer from freezer and remove the metal pan bottom. Remove parchment paper as well. To make the second layer, place cheesecake layer on top of the bottom layer of the carrot cake.
Wait 10 minutes to trim cheesecake layer if necessary. Place the second carrot cake on top of the cheesecake.
Use one frosting recipe that is doubled and frost the sides of the cake first. Then frost the top of the cake.
Refrigerate approximately 30 minutes, then frost with as much of the remaining frosting as necessary. Coat the sides of the cake with toasted pecan if desired. Sprinkle the shredded coconut on the top of the frosted cake.
Refrigerate until ready to serve.