Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, sift together flour, baking powder, and salt.
In a stand mixer, cream 1 cup softened butter and granulated sugar on medium-high speed until light and fluffy (approx. 3-5 minutes).
Add eggs one at a time, beating well after each addition. Incorporate lemon zest, 2 tablespoons of lemon juice, and vanilla extract.
Reduce mixer speed to low. Add the dry ingredients in three parts, alternating with milk, beginning and ending with the flour mixture.
Divide batter evenly between the prepared pans. Bake for 28-32 minutes or until a toothpick inserted into the center comes out clean.
Cool cakes in pans for 10 minutes, then transfer to wire racks to cool completely.
Prepare the frosting by beating 1/2 cup butter with powdered sugar, remaining lemon juice, and heavy cream until light and airy.
Place the first cake layer on a serving plate. Spread a thin layer of buttercream and arrange the sliced strawberries evenly across the surface.
Place the second cake layer on top. Frost the top and sides of the cake with the remaining buttercream.