Preheat the oven to 350 F degrees.Grease a loaf pan with butter or cooking spray. Line the bottom with parchment paper. Grease and flour the pan.Mix together the flour, baking powder, and salt into 1 bowl. In another bowl, whisk together the yogurt, 1 cup sugar, the eggs, lemon zest, and vanilla. Slowly whisk the dry ingredients into the wet ingredients. With a rubber spatula, fold the vegetable oil into the batter, making sure it's all incorporated. Pour the batter into the prepared pan and bake for about 50 minutes, or until a cake tester placed in the center of the loaf comes out clean.Meanwhile, cook the â…“ cup lemon juice and remaining â…“ cup sugar in a small pan until the sugar dissolves and the mixture is clear. Set aside.When the cake is done, allow it to cool in the pan for 10 minutes. Carefully place on a baking rack over a sheet pan. While the cake is still warm, pour the lemon-sugar mixture over the cake and allow it to soak in.Let cool before serving. Sprinkle some powdered sugar over the top or serve with berries.(optional)