01 - Preheat oven to 350°F. Grease and flour a 9-inch round cake pan or line with parchment paper.
02 - Combine sugar, lavender buds, and lemon zest in a small bowl. Rub together with fingers until fragrant and well blended.
03 - Whisk together flour, baking powder, baking soda, and salt in a medium bowl until thoroughly combined.
04 - Beat softened butter with lavender-lemon sugar in a large bowl until light and fluffy. Add eggs one at a time, mixing well after each addition, then stir in vanilla extract.
05 - Fold in flour mixture in three additions, alternating with milk and lemon juice. Begin and end with flour addition, mixing just until incorporated. Avoid overmixing.
06 - Transfer batter to prepared pan, smoothing the surface evenly. Bake for 30–35 minutes until a toothpick inserted into the center emerges clean.
07 - While cake bakes, combine water, sugar, lemon juice, and lavender in a small saucepan. Bring to a simmer, stirring until sugar completely dissolves. Remove from heat and let steep for 5 minutes, then strain through a fine-mesh strainer.
08 - Allow cake to cool in pan for 10 minutes. Transfer to a wire rack. While still warm, brush the lemon-lavender syrup evenly over the entire surface.
09 - Once cake has cooled completely, whisk powdered sugar, lemon juice, and milk until smooth and pourable. Drizzle glaze over the cake and allow to set before serving.