Place an oven rack in the center of the oven. Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
In a food processor, pulse together the flours, arrowroot, sugar, lavender, salt and baking soda.
Add the butter and lemon zest. Pulse until the mixture forms a coarse meal. Add the honey and lemon juice. Pulse until the mixture forms a soft dough. Form the dough into 1-inch round balls and press into discs, about 1 1/2 inches in diameter and 1/4-inch thick. Arrange in a single layer on the prepared baking sheet. Bake until light brown around the edges, 9 to 11 minutes. Cool for 5 minutes. Transfer to a wire rack and cool completely, about 15 minutes.