Preheat oven to 350 degrees. Grease 9x13 inch pan and set aside.
In a small bowl, combine first 7 ingredients - oil through lime zest. Using a whisk, mix thoroughly. Add the squeezed zucchini, mix with a mixing spoon and set aside.
In a medium bowl, combine next 4 ingredients - flour through salt. Mix.
Add the zucchini mixture to the flour and stir until combined.
Pour into prepared 9x13 inch pan and spread evenly.
Bake for 18-22 minutes or until toothpick inserted into the center comes out clean. Note: this cake doesn't get very brown. Check it before you overcook it!
While the cake is baking, combine 4 icing ingredients in a bowl and whisk until smooth. This will take some muscles - or let your cheese come to room temperature first. Wait and frost once the cake has cooled.