Preheat oven to 350°F (175°C) and grease or line a 9x5 loaf pan with parchment paper.
In a bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, beat butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in vanilla extract, lemon zest, and lemon juice.
Add sourdough discard and Greek yogurt, mixing until smooth.
Add half of the dry ingredients, mix gently, then add milk, followed by the remaining dry ingredients. Mix just until combined.
Pour batter into prepared pan and smooth the top.
Bake for 50 to 60 minutes until a toothpick inserted comes out with a few moist crumbs.
Cool in the pan for 10 to 15 minutes, then transfer to a wire rack to cool completely.
Mix powdered sugar and lemon juice to make glaze.
Drizzle glaze over cooled loaf and let set before slicing.