Preheat your oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.

In a large bowl, whisk together the sifted flour, sugar, baking powder, and salt.

In a separate bowl, whisk together the milk, lemon juice, lemon zest, and vanilla extract.

In a stand mixer, cream the softened butter until light and fluffy. Add the eggs one at a time, beating well after each addition.

Gradually add the dry ingredients to the butter mixture, alternating with the wet ingredients, beginning and ending with the dry.

Divide the batter evenly among the prepared cake pans and bake for 25-30 minutes.

Let the cakes cool in their pans for 10-15 minutes before inverting onto a wire rack to cool completely.

While cakes cool, make the lemon simple syrup by combining sugar and water in a saucepan, heating until sugar dissolves, then stir in lemon juice and let cool.

For the frosting, beat the softened butter until light and fluffy, then gradually add powdered sugar, mixing until incorporated. Beat in lemon juice and zest, then add heavy cream until desired consistency is reached.

Once the cake layers are cool, level them if necessary. Brush each layer with lemon simple syrup, then assemble the cake with frosting between layers and on the outside.

Chill the cake for 15-20 minutes to set the crumb coat, then apply the final layer of frosting and garnish as desired.