Preheat the oven to 350˚F, convection setting. Grease one loaf pan and set it aside. If you want to be able to easily remove the bread for it for slicing, this is critical.
In a large bowl beat the eggs. Mix in the yogurt, oil, and sugars. Then mix in the shredded zucchini, oregano, lemon zest, and lemon juice. Set aside.
In a separate bowl whisk together the flour, baking soda, baking powder, and salt.
Stir the dry ingredients into the wet ingredients. Stir in the rice.
Once the batter is well combined pour into the loaf pan.
Bake for one hour, give or take a few minutes, until a tester inserted comes out clean. My loaves took one hour and five minutes.
Remove from the oven and let sit for 10 minutes. Using a sharp knife, cut around the sides of the bread and gently edge it away from the sides. Place one hand over the top of the bread, and flip the loaf pan upside down. It should rest in your hand. Immediately flip it over onto a cooling rack. Let it come to room temperature, or close to it, before slicing. This is a very moist bread and will slice well when cooled, but not so well hot from the oven.