01 - Preheat oven to 350°F. Grease and line three 8-inch round cake pans with parchment paper.
02 - In a bowl, whisk together flour, baking powder, baking soda, and salt.
03 - In a separate large bowl, beat butter, sugar, and lemon zest until light and fluffy.
04 - Beat in eggs one at a time, then add lemon juice and vanilla.
05 - Alternate adding flour mixture and buttermilk, beginning and ending with flour. Mix until just combined.
06 - Divide batter evenly among prepared pans. Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
07 - Cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
08 - In a saucepan, combine strawberries, sugar, and lemon juice. Cook over medium heat until strawberries release juices, about 5 minutes.
09 - Mix cornstarch and water; stir into strawberries. Cook, stirring constantly, until thickened, 1 to 2 minutes. Remove from heat and cool completely.
10 - Beat cream cheese and butter until smooth. Gradually add powdered sugar, then lemon juice, zest, vanilla, and salt. Beat until fluffy.
11 - Place one cake layer on a serving plate. Spread half of the strawberry filling over the top, avoiding the edges. Add a layer of frosting to prevent the filling from seeping out.
12 - Repeat with the second layer, then top with the final cake layer.
13 - Frost the top and sides with remaining lemon cream cheese frosting.
14 - Chill cake for at least 30 minutes before slicing for neat layers.