Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the granulated sugar and eggs together until pale and fluffy, about 2-3 minutes.
Add the Greek yogurt, vegetable oil, fresh lemon juice, lemon zest, and vanilla extract to the egg mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer it to a wire rack to cool completely.
Once the cake is cooled, whisk the powdered sugar with 1 tablespoon of fresh lemon juice to make a glaze. Drizzle the glaze over the top of the loaf cake.
Slice and serve.