Preheat the oven to 350 degrees F. Grease and flour two 8-inch cake pans. Set aside.
In a large mixing bowl, beat the butter and sugar until fluffy, about 2-3 minutes. Add in the eggs, lemon juice, lemon zest, and vanilla. Beat on medium-low speed for 1 minute.
Pour in the cake mix and fold into the wet ingredients using a rubber spatula until well combined. Fold in the grated zucchini until evenly mixed. Divided the cake batter between the two prepared cake pans.
Bake for 25 minutes, or until a cake tester inserted in the center comes out clean.
Remove from the oven and cool for 10 minutes in the pan. Then run a knife around the edge and turn the cakes out onto a wire rack. Allow to cool completely.
Frosting
Add 1 cup of powdered sugar, the butter, lemon juice, and lemon zest to a large mixing bowl. Beat together until smooth. Continue adding the powdered sugar, 1 cup at a time, mixing after each addition. Set aside.
Assembly
If needed, level the tops of the cakes. Place 1 cake layer, bottom side down, onto a cake stand or platter. Spread about 1/3 of the frosting over the top of the cake in an even layer with an offset spatula.
Place the second cake, bottom side up, over the first layer. Frost the top and sides of the cake so they are coated. I like to reserved about 1/2 cup of frosting to pipe rosettes on top of the cake. Then, garnish the top with twisted lemon slices, if desired.
Notes
The frosting recipe makes enough to completely coat the top and sides. If you want rosettes on top (as shown) the sides will get a thinner coat and have a lightly "naked" cake or "crumb coat" look, which I actually love.