Preheat oven to 350°F (175°C). Grease three 8-inch round cake pans, line bottoms with parchment paper, and lightly flour the sides.

In a large bowl, whisk together the cake flour, sugar, baking powder, and salt until evenly combined.

Add the softened butter to the dry ingredients and beat on medium speed for 3 minutes until the mixture resembles coarse sand with pea-sized butter pieces throughout.

In a separate bowl, whisk together eggs, buttermilk, lemon juice, lemon zest, and vanilla until smooth. Pour half of this mixture into the flour mixture and beat on medium speed for 1 minute, scraping down the bowl halfway through.

Add the remaining wet ingredients and beat for another 30 seconds until just combined and smooth — do not overmix or the cake will be tough.

Divide batter evenly among the three prepared pans (about 2 cups each) and smooth the tops. Bake for 23-26 minutes until a toothpick inserted in the center comes out clean and the edges just begin to pull away from the pan.

While cakes bake, make the raspberry syrup: combine raspberries, water, and 1/3 cup sugar in a small saucepan over medium heat. Simmer for 8-10 minutes, mashing berries occasionally, until slightly thickened. Strain through a fine-mesh sieve and let cool completely.

Cool cakes in pans for 10 minutes, then turn out onto wire racks to cool completely. Once cool, wrap and freeze for 20 minutes for easier frosting.

For the frosting, beat cream cheese and butter together on medium-high speed for 3 minutes until completely smooth and fluffy. Add powdered sugar one cup at a time, beating well after each addition. Mix in vanilla, then gently fold in 3/4 cup fresh raspberries.

To assemble, place one cake layer on a serving plate and poke several small holes with a toothpick across the surface. Brush with one-third of the raspberry syrup, then spread with 1 cup of frosting. Repeat with second layer, then top with final layer and frost the top and sides smoothly. Garnish with remaining fresh raspberries and serve.