Preheat and Prep. Start by preheating your oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper for easy removal.
Mix Dry Ingredients. In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
Combine Wet Ingredients. In a large bowl, whisk together the yogurt, sugar, eggs, lemon zest, lemon juice, oil, and vanilla extract until smooth and fully combined.
Combine Wet and Dry. Gently fold the dry ingredients into the wet mixture using a spatula or wooden spoon. Mix until just combined. Don’t overmix or the cake may be dense.
Bake the Cake. Pour the batter into the prepared loaf pan and smooth the top. Bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Cool and Glaze. Let the cake cool in the pan for 10–15 minutes, then transfer to a wire rack. Once cool, whisk together powdered sugar and lemon juice to make a simple glaze. Drizzle over the cooled cake and let it set before slicing.