Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large bowl, sift together the flour, cocoa powder, baking powder, baking soda, and salt. Set aside.
In a separate bowl, whisk together granulated sugar and brown sugar. Add the eggs, one at a time, beating well after each addition.
Stir in the buttermilk, lemon juice, lemon zest, melted butter, and vanilla extract. Mix until combined.
Gradually add the dry mixture to the wet mixture, stirring just until combined. Do not overmix.
Pour the batter evenly into the prepared cake pans. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.
In a large bowl, beat the softened butter with an electric mixer until smooth. Gradually add the powdered sugar, 1 cup at a time, beating until fluffy. Add the lemon juice, lemon zest, and heavy cream. Mix until smooth and creamy. Add yellow food coloring, if desired.
Once the cakes are completely cooled, spread a layer of lemon buttercream on top of the first cake. Place the second cake on top and frost the entire cake with the remaining buttercream.
Serve and enjoy your delicious lemon chocolate cake!