Preheat oven to 350°F (175°C). Grease or line a standard loaf pan with parchment paper.
Cream butter and sugar in a large bowl until light and fluffy.
Add eggs one at a time, mixing well after each addition. Stir in sourdough starter, milk, lemon zest, lemon juice, and vanilla extract.
In a separate bowl, whisk together dry ingredients: flour, baking soda, baking powder, and salt.
Gradually fold dry ingredients into wet ingredients until just combined. Do not overmix.
Pour batter into prepared loaf pan and smooth the top.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, loosely tent with foil during the last 10–15 minutes.
Allow loaf to cool in the pan for 10–15 minutes, then transfer to a wire rack to cool completely before glazing.
For the glaze, whisk powdered sugar and lemon juice until smooth. Drizzle over cooled loaf.