Start by peeling, coring, and cutting the pineapple into small chunks. Place the pineapple and any collected juice in a saucepan. Add the sugar and lemon juice, then stir to combine.
Bring the mixture to a boil, then reduce the heat to low-medium and simmer, stirring occasionally, until the pineapple becomes soft and translucent, about 20 minutes. Carefully remove 1 cup of the syrup and set it aside to soak the cake layers.
Using a hand blender or food processor, blend the pineapple until slightly chunky. Continue cooking the mixture until it thickens, becomes glossy, and takes on a light golden color, about 70 minutes. Allow both the jam and the reserved syrup to cool completely before using..
For the Cake, adjust the oven rack to the middle position and preheat the oven to 350°F (175°C). Grease three 9-inch round cake pans, line with parchment paper, grease parchment, then flour pans.
In a stand mixer fitted with the paddle attachment, beat butter, oil, vanilla, coconut extract, and sugar on medium-high for 5 minutes, until very pale and fluffy.
Add eggs 2 at a time, mixing for 30 seconds after each addition. Scrape bowl as needed.
Add self-raising flour and unsweetened coconut flakes. Mix on low just until no dry spots remain.
Add unsweetened coconut cream on low until just combined. Do not overmix.
Divide batter evenly among prepared pans. Smooth the tops and tap the pans a few times to release any air bubbles. Bake until the cakes are golden and a paring knife inserted in the centers comes out clean, about 26 minutes, rotating the pans halfway through baking.
Let cakes cool in pans for 10 to 15 minutes. Turn out onto racks, discarding parchment. Using a pastry brush, lightly brush each layer with the reserved pineapple syrup, about 1–2 tablespoons per layer, being careful not to oversoak—you want the cakes moist, not soggy.
For the Frosting (Coconut Cream Cheese Frosting), in a stand mixer fitted with the paddle, mix butter and sugar on low speed until combined, about 30 seconds.
Increase speed to medium-high and beat until pale and fluffy, about 2 minutes.
Add sweetened cream of coconut, vanilla, and salt. Beat until smooth, about 30 seconds.
Add cream cheese, one piece at a time, beating until incorporated, about 1 minute.
Stir in coconut flakes. Refrigerate until ready to use.
To assemble, place one cooled cake layer on a serving platter. Spread a generous, even layer of pineapple jam over the top.
Stack the second cake layer on top and spread another generous layer of pineapple jam.
Place the final cake layer on top. Spread a thin layer of frosting (crumb coat) over the top and sides to seal in crumbs. Chill for 20–30 minutes.
Apply a smooth, even layer of frosting over the top and sides using an offset spatula and bench scraper.
Hold an icing comb in the design of your choice firmly against the side of the cake, teeth resting at the base. Keep your hand steady as you turn the cake to create an even pattern.
If the comb gathers excess frosting, wipe it clean and repeat. Finally, run the comb gently across the top to form a spiral. Clean after each pass for sharp, neat lines.