Preheat oven to 350 degrees Grease a 10 x 15-inch sheet pan with nonstick cooking spray and set aside. If you want slightly thicker bars you can use a 9x13-inch pan.
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, combine the granulated sugar and lemon zest. Rub together with your fingers until fragrant. Add the oil, eggs, lemon juice, and vanilla extract. Whisk until smooth. Stir in the grated zucchini.
Add the dry ingredients and stir until just combined. Don’t over mix.
Pour the batter evenly into the prepared sheet pan. Bake for 25 to 30 minutes, or until the bars are set. Don’t over bake. Let the bars cool completely.
While the bars are cooling, make the lemon cream cheese frosting. Using a stand mixer fitted with a paddle attachment, beat the cream cheese and butter together on medium speed until smooth and no lumps remain, about 2 to 3 minutes. Reduce the mixer speed to low, then add 3 cups powdered sugar, lemon juice, lemon zest, and pinch of salt. Once the sugar begins to incorporate, increase the mixer to high speed and beat for 2 minutes or until smooth. If the frosting is too thin, you can add more powdered sugar, until desired consistency is reached.
Spread the lemon cream cheese frosting evenly over the cooled bars. Cut into squares and serve.