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 to infuse the sugar with floral and citrus oils.
03 - Whisk together flour, baking powder, baking soda, and salt in a medium bowl until well blended.
04 - In a large bowl, cream the butter with the lavender-lemon sugar until light and fluffy. Beat in eggs one at a time, then add vanilla extract.
05 - Mix in the flour mixture in three additions, alternating with milk and lemon juice, starting and ending with flour. Mix just until combined—do not overmix.
06 - Pour batter into the prepared pan and smooth the top. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean.
07 - While the cake bakes, combine water, sugar, lemon juice, and lavender in a small saucepan. Bring to a simmer, stirring until sugar dissolves. Let steep for 5 minutes, then strain.
08 - Cool cake in the pan for 10 minutes. Remove to a wire rack. While still warm, brush the cake generously with the lemon-lavender syrup.
09 - When the cake is completely cool, whisk powdered sugar, lemon juice, and milk until smooth. Drizzle the glaze over the cake and allow to set before serving.