Preheat the oven to 350 ° F. Prepare a bread pan by lining with parchment paper. Grate zucchini and set aside.
In a large mixing bowl, combine the eggs, oil, greek yogurt, vanilla, lemon zest, and lemon juice. Whisk together until smooth.
Add in the sugar, salt, flour, and baking powder, and poppyseeds and fold in. Add in grated zucchini and mix until just combined and there are no flour pockets left.
Transfer batter to baking pan. Bake for 55-60 minutes, then check doneness with an inserted toothpick. If clean, remove bread and cool for 20-30 minutes on cooling rack before icing.
For the Glaze:
In a small bowl combine powdered sugar, lemon zest, juice, and vanilla. Stir until smooth. When loaf has cooled, drizzle over the top of the loaf. Wait for 30-60 minutes for the glaze to dry a little before slicing, or serve fresh.
Notes
Store at room temperature in an airtight container for up to 3 days. Freeze with no icing for up to 3 months, then thaw and glaze before serving.