Preheat the oven to 350°F. Grease a loaf pan with cooking spray or line with parchment paper for easy removal.
In a large bowl, whisk together the flour, baking powder, salt, and sugar until well combined.
In a medium bowl, whisk together the melted butter, lemon juice, eggs, sourdough discard, and milk until smooth.
Pour the wet ingredients into the dry ingredients and mix on low speed with a hand mixer or stand mixer until just combined. Avoid overmixing for a tender crumb.
Pour the batter into the prepared loaf pan, smooth the top, and bake for about 50 minutes or until a toothpick inserted in the center comes out clean.
While the loaf bakes, whisk together the powdered sugar and lemon juice in a small bowl until smooth.
Once baked, let the cake cool in the pan for 10–15 minutes. Spread the glaze over the top while still warm, then let the loaf cool completely on a wire rack before slicing and serving.