Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.
In a large bowl, beat softened butter and sugar until light and fluffy.
Add egg, lemon juice, lemon zest, and vanilla. Mix until smooth.
In a separate bowl, whisk together almond flour, tapioca flour, salt, and baking soda.
Gradually stir dry ingredients into the wet mixture.
Fold in the dried lavender buds.
Scoop tablespoon-sized portions of dough onto the baking sheet. Flatten slightly.
Bake for 10–12 minutes, until edges are lightly golden. Cool on pan for 5 minutes before transferring to a rack.
Prepare the glaze by whisking powdered sugar, milk, lemon juice, and crushed lavender in a small bowl.