Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan or line it with parchment paper for easy removal.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
Add the eggs, vanilla extract, lemon zest, and lemon juice to the butter mixture. Mix until well combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Fold in the grated zucchini gently until evenly distributed throughout the batter.
Pour the batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
While the bars are baking, prepare the glaze by whisking together the powdered sugar, lemon juice, and lemon zest in a small bowl until smooth.
Once the bars are done baking, allow them to cool in the pan for about 10 minutes before transferring them to a wire rack to cool completely.
Drizzle the glaze over the cooled bars before cutting them into squares.