Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan and set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well combined.
In a large bowl, whisk the granulated sugar and eggs together until the mixture is light and fluffy, about 2-3 minutes.
Add the Greek yogurt, vegetable oil, lemon zest, lemon juice, and vanilla extract to the egg mixture. Whisk until smooth and fully combined.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven 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.
Transfer the cake to a wire rack to cool completely.
Once the cake is completely cooled, whisk the powdered sugar with 1-2 tablespoons of fresh lemon juice until smooth to create a glaze.
Drizzle the lemon glaze over the top of the loaf cake and let it set before slicing and serving.