Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan or line it with parchment paper.
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 Greek yogurt and granulated sugar until smooth and creamy.
Add the eggs one at a time to the yogurt mixture, whisking well after each addition.
Whisk in the vegetable oil, lemon zest, lemon juice, and vanilla extract until fully incorporated.
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 for 45 to 50 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the loaf from the oven and let it cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before slicing and serving.