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Into a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder and salt. In a separate small bowl, whisk together the vegetable oil, lemon zest and eggs. Using a rubber spatula, stir the egg mixture into the flour mixture until just combined. Fold in the shredded zucchini and chopped walnuts. Spread the cake batter evenly in the desired cake pans.
Bake until a toothpick inserted into the center comes out clean and the cake springs back slightly when touched and just pulls away from the side of the pan, 30 to 40 minutes.
Remove the cakes from the pans when completely cooled.