Prepare the Oven and Pan - Preheat the oven to 350 degrees Fahrenheit. Grease and flour the pan.
Combine Dry Ingredients - In a large bowl, combine flour, baking soda, baking powder, and salt.
Beat Ingredients - Using an electric mixer, beat together the sugar, oil, eggs and half of the cream cheese. Gradually add in the dry ingredients, mixing every time.
Add the Zucchini and Lemon - Grate the zucchini and add it to the mix. Add the lemon zest and three tablespoons of lemon juice, mixing thoroughly.
Bake the Bread - Bake the bread for 40-45 minutes. Stick a toothpick to check if the bread is done if the toothpick comes out clean the bread is done. Cool for 15 minutes then remove the bread from the pan and let it cool on the wire rack.
Make the Drizzle - While the bread is baking, mix the powdered sugar, remaining lemon juice and remaining cream cheese together. Mix until the drizzle is smooth. Allow the bread to cool completely before adding the drizzle, then let the bread stand until the drizzle is firm before cutting.
For an extra lemon kick, add some lemon zest to the top before serving. This is a delicious sweet bread that is great for parties.