For the lemon cake: Preheat the oven to 350 degrees F. Butter two 9-inch round cake pans, then insert a round of parchment cut to fit just inside the bottom of each pan. Butter the parchment, then flour the pans, tapping out any excess flour.
In a medium bowl, stir together the cake flour, baking powder and salt.
Using an electric, standing or hand mixer, beat the butter and granulated sugar until very fluffy and pale yellow, about 2 minutes. Add the eggs 1 at a time, then add the vanilla followed by the lemon zest and juice--the mixture may appear to break apart a bit or curdle, but it will come back together when the flour is added, so don't panic! Add about a third of the flour mixture and mix until just barely incorporated, then add half of the milk and blend. Repeat with one-third of the flour mixture, the rest of the milk and the rest of the flour mixture and blend until the ingredients are just completely incorporated.
Scrape down the sides of the bowl in the middle of this process. Scrape the batter into the prepared pans, dividing it evenly and smoothing the tops. Bake until a wooden skewer or toothpick inserted into the center of the cake comes out clean, 22 to 26 minutes. Cool the cakes in the pans on a wire rack for 15 minutes, then run a knife around the insides of the pans to make sure the sides don't stick, place a wire rack over the top of each pan and invert the cake onto the wire rack. Peel off the parchment and cool completely.
For the lemon filling: While the cakes are baking, make the lemon curd. Whisk the granulated sugar, lemon juice, butter, egg yolks and salt in a small nonreactive saucepan. Place the pan over medium-low heat and cook, whisking constantly, until thickened, about 10 minutes. Place the lemon curd in a small bowl, press a piece of plastic wrap on top of the surface and place it in the refrigerator to chill for at least 2 hours and up to a week.
Briskly stir the lemon zest into the chilled curd to blend well. In a medium bowl, beat the heavy cream just until stiff peaks form. Gently fold into the lemon curd with a rubber spatula. Refrigerate for at least 1 hour but not more than 6 hours.
For the lemon frosting: In a large bowl with an electric, standing or hand mixer, beat the confectioners' sugar with the butter on low speed until combined, then turn the beater speed to high and add the cream and lemon zest and juice. Beat until fluffy.
To assemble the cake, place each cake layer upside down on a round of cardboard or a flat plate. Using an offset spatula or butter knife, frost the top and sides of each cake layer with a very thin layer of the lemon frosting. Place the cake layers in the freezer for 15 minutes or in the refrigerator for 30 minutes to firm up the thin layer of frosting.
Place the bottom layer of cake on the platter that you will be serving it on and tuck thick strips of wax or parchment paper under the edges of the cake to keep the platter clean. Spread the lemon filling over the bottom layer, leaving a 1/2-inch border all around so the filling has a bit of room to spread when you place the second layer on top. Cover the filling with the raspberries, then place the second layer of cake on top.
Frost the cake with the rest of the frosting. The cake will keep for up to 4 days in the refrigerator, though it's best within a day of making. Bring to room temperature before serving.