To Make the Lemon Cake:
Preheat the oven to 350°F (180°C). Butter, flour, and line with parchment three 8-inch (20cm) round cake pans. Set aside.
With an electric mixer, cream the butter and sugar until light and fluffy, then add the eggs one at a time until fully combined.
In a measuring cup with a pour spout, combine the milk, lemon juice, oil, lemon extract, and lemon zest. Gradually add the liquid to the butter mixture until thoroughly mixed.
In a small bowl, whisk together the flour, cornstarch, baking powder, baking soda, and salt. Gradually beat into the batter just until evenly combined.
Divide the batter between your prepared pans and bake for 25-30 minutes, until a skewer inserted in the center comes out clean.
Let cool for 10 minutes in the pans before inverting onto a cooling rack to cool completely.
To Make the Lemon Buttercream Frosting:
While the cake is cooling, beat the butter until light and fluffy with an electric mixer, then gradually add the powdered sugar. Beat until fully combined.
Pour in the lemon juice, cream or milk, and lemon zest and beat until combined.
When the cake is thoroughly cooled, level your layers and frost.
Store this cake at room temperature in an airtight container for up to 2 days.