Preheat oven to 350°F and grease a 9x5 loaf pan. I also line mine with parchment paper for easy removal after baking.
In a large mixing bowl, whisk together the eggs, oil, lemon zest, lemon juice, and sugar until well combined.
Whisk in the baking powder, baking soda, and salt.
Fold in the flour, and mix just until everything is well incorporated and there are no dry pockets of flour left.
Gently fold in the shredded zucchini and poppy seeds.
Pour the batter into your prepared loaf pan, and smooth it out a little bit so that it fills the pan evenly. Bake for about 60-65 minutes until risen, turning golden on top, and a toothpick inserted into the center comes out without wet batter clinging to it.
Allow the bread to cool in the pan for about 10 minutes before removing and allowing to cool fully on a baking rack.
Once the bread is cool, make the glaze by whisking together the powdered sugar with the lemon juice until pourable, but still relatively thick. You can use all lemon juice for a nice tart glaze, or a mixture of lemon juice and milk or cream to your taste for a slightly less tart glaze.
Pour the glaze over the cooled cake and use the back of a spoon or a butter knife to gently spread it over the top of the cake. Allow the glaze to harden before slicing.