01 - Preheat oven to 350°F. Grease and line three 8-inch round cake pans with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
03 - In a large bowl, beat butter and sugar until light and fluffy, about 3 minutes. Add eggs one at a time, beating well after each. Mix in lemon zest and vanilla.
04 - Combine lemon juice and milk. With mixer on low, alternately add flour mixture and lemon-milk mixture to the butter mixture, beginning and ending with flour. Mix until just combined.
05 - Divide batter evenly among prepared pans. Bake for 22-26 minutes, or until a toothpick inserted into the center comes out clean. Cool in pans for 10 minutes, then transfer to wire racks to cool completely.
06 - In a saucepan over medium heat, combine raspberries, sugar, and lemon juice. Cook, stirring, until raspberries break down, about 5-7 minutes. Stir in cornstarch slurry. Cook 2-3 minutes more, until thickened. Cool completely.
07 - In a large bowl, beat cream cheese and butter until smooth. Add powdered sugar gradually, beating until fluffy. Mix in lemon juice, zest, vanilla, and salt until smooth.
08 - Place one cake layer on a serving plate. Spread half the raspberry filling evenly over the top, leaving a 1/2-inch border. Pipe a ring of frosting around the edge to contain the filling. Top with second cake layer and repeat. Place third cake layer on top, then frost the top and sides with the lemon cream cheese frosting.
09 - Decorate with fresh raspberries and lemon zest or slices if desired. Chill for 30 minutes before slicing for best results.