Preheat oven to 350°F. Spray a bundt pan or 9x13-inch baking pan with nonstick cooking spray.
In a large bowl, mix together the sugar and lemon zest until the sugar is moistened and the zest is thoroughly incorporated.
Add in vegetable oil, eggs, lemon juice, and vanilla extract and mix with a hand mixer on medium speed until all of the ingredients are incorporated.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the flour mixture to the wet ingredients and mix until just combined. Fold in the zucchini.
Spoon batter into prepared pan. Bake a bundt cake for 45-50 minutes and a 9x13-inch cake for 35-40 minutes or until a tester inserted into the center comes out clean. Allow cake to cool completely.
In a medium bowl, prepare the glaze by mixing together the melted butter, powdered sugar, vanilla and lemon juice. Whisk until smooth and drizzle over cooled cake. Glaze will harden slightly.