Preheat oven to 350°F (177°C). Grease three 8-inch cake pans, line with parchment paper rounds, then grease the parchment paper.

Whisk the flour, baking powder, baking soda, and salt together. Set aside.

Using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the butter and sugar together on high speed until smooth and creamy, about 3 minutes.

Beat in the eggs and vanilla extract on high speed until combined, about 2 minutes.

With the mixer on low speed, add the dry ingredients just until combined.

With the mixer still running on low, add the milk, lemon zest, and lemon juice and mix just until combined.

Divide the batter evenly between the prepared cake pans. Bake for around 21–26 minutes or until the cakes are baked through.

Allow cakes to cool completely in the pans set on a wire rack.

In a large bowl using a hand-held mixer or stand mixer fitted with a whisk or paddle attachment, beat the butter on medium speed until creamy, about 2 minutes.

Add the cream cheese and beat until completely smooth and combined.

Add confectioners’ sugar, lemon juice, and vanilla extract with the mixer running on low. Increase to high speed and beat for 3 minutes.

Using a large serrated knife, slice a thin layer off the tops of the cakes to create a flat surface.

Place 1 cake layer on your cake stand, cake turntable, or serving plate. Evenly cover the top with about 1 cup of frosting.

Top with 2nd cake layer and evenly cover the top with about 1 cup of frosting.

Top with the third cake layer. Spread the remaining frosting all over the top and sides.

Refrigerate for at least 30–45 minutes before slicing.