Preheat oven to 350°F (177°C). Grease two 9-inch round cake pans, line bottoms with parchment, and dust with flour.

In a medium bowl, whisk together flour, baking powder, baking soda, and salt.

In a small bowl, combine ground lavender buds and lemon zest with 1 tablespoon of the sugar; rub together with fingers to release oils. Set aside.

In a large bowl, beat butter and remaining sugar on medium speed until light and fluffy, about 3 minutes. Add eggs one at a time, beating well after each. Beat in vanilla.

Reduce speed to low. Add flour mixture in three additions, alternating with buttermilk, beginning and ending with flour. Mix until just combined. Fold in lemon juice and the lavender-zest mixture.

Divide batter evenly between prepared pans. Bake for 22-25 minutes, until a toothpick inserted in center comes out clean or with a few moist crumbs. Cool in pans 10 minutes, then turn out onto a rack to cool completely.

For the lemon curd: In a heatproof bowl, whisk lemon juice, sugar, egg yolks, egg, and salt. Set over a pot of simmering water (bowl should not touch water). Whisk constantly until thickened, about 8-10 minutes, reaching 170°F (77°C) on an instant-read thermometer. Remove from heat; whisk in butter pieces until smooth. Strain through a fine-mesh sieve. Press plastic wrap directly onto surface; chill at least 2 hours.

For the lavender buttercream: Beat butter on medium-high until creamy, about 2 minutes. Gradually add powdered sugar, beating on low. Add cream, vanilla, and ground lavender; beat on medium-high for 3 minutes until light and fluffy. Add milk as needed for spreadable consistency.

To assemble: Place one cake layer on a serving plate. Spread a thin layer of buttercream, then pipe a ring of buttercream around the edge. Fill center with lemon curd (about 1/3 cup). Top with second layer. Crumb coat, then chill 20 minutes. Apply final coat of buttercream. Decorate as desired.