Spray or butter a standard loaf pan. Line with parchment paper, if desired. Preheat oven to 350°F (175°C).
To the bowl of a stand mixer, add the butter, sugar and lemon zest. Beat at high speed with the paddle attachment until butter is pale and fluffy (about 5 minutes). Add eggs, one at a time, beating until incorporated.
In a small bowl, whisk together yogurt, lemon juice and vanilla. In another small bowl, whisk together flour, baking powder, baking soda and salt.
Mixing by hand with a spatula or wooden spoon, add ⅓ of the flour mixture to the butter mixture. Stir until just mixed in. Now add ½ of the yogurt mixture, stirring in gently. Repeat until all the flour and yogurt has been added.
Pour into prepared loaf pan. Bake for 35-40 minutes until lightly golden brown and a wooden skewer or toothpick inserted into the center comes out fairly clean.
While cake bakes, make the lemon glaze. In a small saucepan, add the lemon juice, sugar and water. Bring to a gentle boil and simmer over low heat until slightly thickened (about 5 minutes). When cake is done, cool on a wire rack for 15 minutes. Remove from pan. Pour syrup over, spreading over top with a spoon and allow to cool completely.