Let’s break down the process into manageable steps.

For the Cake:

1. Preheat and Prepare Pans: Preheat the oven to 350°F (175°C). Spray 2 (8-inch) round cake pans with baking spray with flour. (Alternatively, butter and flour the pans.) Line the bottoms of the pans with parchment paper and spray (or butter) again.   
2. Whisk Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
3. Combine Wet Ingredients: In a large bowl, whisk together the granulated sugar, melted butter, vegetable oil, and lemon zest until combined.
4. Add Eggs: Whisk in the eggs, one at a time, until lightened in color, about 1 minute.
5. Add Remaining Wet Ingredients: Whisk in the buttermilk, lemon juice, and vanilla.
6. Combine Wet and Dry: Add the flour mixture in 3 parts, whisking to combine after each addition.
7. Divide Batter: Evenly divide the batter between the prepared pans. Tap the pans a few times on a kitchen towel on your countertop to level the surface and remove air bubbles.   
8. Bake: Bake until a toothpick inserted in the center comes out with only a few crumbs, 30 to 35 minutes.
9. Cool. Transfer to a cooling rack. Let cool in the pans for 10 minutes, then turn out onto a cooling rack to cool completely, about 1 1/2 hours.   

For the Jam Filling:

1. Make Cornstarch Slurry: Meanwhile, in a small bowl, whisk together the cornstarch and 1 tablespoon water.
2. Heat Jam: In a small saucepan, heat the jam over medium heat until pourable and smooth, about 1 minute.
3. Thicken Jam: Remove the jam from the heat and whisk in the cornstarch mixture. Return the saucepan to medium heat and bring the mixture to a boil. Boil, stirring constantly, until no longer cloudy with cornstarch and a rubber spatula dragged through the mixture reveals the bottom of the pan for a few seconds before the jam flows back together, 2 to 3 minutes.
4. Cool: Transfer the thickened mixture to a bowl and let it cool completely.

For the Frosting:

1. Beat Butter: To the bowl of a stand mixer fitted with the paddle attachment, add the butter. Beat on medium speed until smooth, about 1 minute.   
2. Add Jam and Flavorings: Scrape down the bottom and sides of the bowl. Add the jam, lemon juice, and vanilla, and beat on low speed until just combined, 30 seconds. The mixture might appear broken but that is okay.   
3. Beat Jam and Butter: Increase the speed to medium and beat until the butter and jam are no longer separated, 1 to 2 minutes.
4. Add Powdered Sugar: Gradually add the powdered sugar, and beat on low speed until combined.
5. Beat Until Fluffy: Scrape the bottom and sides of the bowl. Increase the speed to medium and beat until smooth and fluffy, 3 to 4 minutes.

Assemble the Cake:

1. First Layer and Frosting Barrier: Place 1 cake layer on a cake plate. Spread about ½ cup of frosting over the top; this will be a barrier to prevent the cake from absorbing the jam filling.   
2. Pipe Frosting Border: Spoon about ½ cup of the frosting into a zip-top bag and cut a ¾-inch opening in one corner. Alternatively, use a pastry bag fitted with a ¾-inch tip. Pipe a thick border around the edge of the frosted cake layer; this will prevent the jam filling from leaking out the sides of the cake.
3. Add Jam Filling: Stir the jam filling to loosen it up. Spread the filling on top of the cake within the frosting border, leaving about ½ inch of space between the filling and the border.   
4. Add Second Layer: Top with the second cake layer.
5. Crumb Coat: Spread about 1 cup of frosting in a thin layer over the top and sides of the cake.
6. Chill: Chill the cake, uncovered, in the refrigerator for 30 minutes or in the freezer for 10 minutes to set the frosting and the filling.   
7. Final Frosting: Use the remaining frosting to frost the top and sides of the cake.
8. Decorate (Optional): Decorate the cake with the raspberries or serve on the side, if you like.

These instructions are detailed and long, but the cake will be worth it.