Preheat the oven to 350°F (180°C). Grease a 9x5-inch loaf pan and line it with parchment paper, letting the edges overhang for easy removal.

In a medium bowl, whisk the flour, baking powder, and baking soda together. Set aside.

In a large bowl, combine the granulated sugar, lemon zest, and lavender. Rub the zest and lavender into the sugar with your fingertips until fragrant and the sugar is pale yellow.

Add the softened butter to the sugar mixture and cream with an electric mixer on medium-high until light and fluffy, about 2 to 3 minutes.

Beat in the eggs one at a time, scraping the sides of the bowl after each addition. Mix in the lemon juice until fully combined.

Mix half of the flour mixture into the batter until just combined. Add the sourdough discard and milk, mixing until smooth. Fold in the remaining flour mixture until no streaks of flour remain.

Scrape the batter into the prepared loaf pan and smooth the top.

Bake for 50 to 60 minutes, until the top is golden brown and a skewer inserted in the center comes out clean. If the top browns too quickly, tent loosely with foil.

Let the loaf cool in the pan for 15 minutes, then lift it out using the parchment overhang and transfer to a wire rack. Let cool completely before glazing.

For the glaze, whisk the powdered sugar, 3 tablespoons of milk, and lavender extract in a bowl until smooth. Add the purple food coloring and adjust with extra milk or powdered sugar to reach a drizzling consistency.

Drizzle the glaze over the cooled loaf, let it set for a few minutes, then slice and enjoy.