Simmer lavender, sugar, and water; strain and cool syrup.
Cream butter and sugar, add eggs, zest, lemon juice, syrup, vanilla.
Whisk dry ingredients, then alternately fold in flour and milk.
Pour into greased pan, tap to release bubbles.
Bake 45–50 min at 350°F until toothpick clean.
Brush warm cake with syrup, cool, then glaze.