Preheat oven to 350°F. Oil and flour a 9 x 13-inch pan and set aside.
In a large bowl, sift together the flour, sugar, baking powder, baking soda and salt. In another bowl, whisk together the water, lemon juice, oil, vinegar, vanilla extract and lemon zest. Combine the wet and dry ingredients and stir until just combined.
Pour the batter into the prepared pan. Bake for 20-25 minutes, or until an inserted toothpick comes out clean.
While the cake is baking, prepare the frosting. Using a stand or hand-held mixer, blend the butter and cream cheese.
Sift together the confectioner’s sugar with the cornstarch. If you don’t have confectioner’s sugar on hand, you can use 2 cups of regular sugar and process the sugar with the cornstarch in a blender for 1 minute. Then scrape down the sides and blend for an additional 30 seconds.
Add half of the sugar/cornstarch mixture to the butter/cream cheese mixture and beat well to combine. Add the remaining sugar/cornstarch mixture along with the lemon juice, lemon zest, and vanilla extract and continue to beat until the frosting is light and fluffy.
Let the cake cool completely before frosting.