Preheat oven to 350°.
Line 2 baking sheets with parchment or baking liners.
Grind lavender buds in a clean coffee grinder or mortar and pestle. Set aside.
In a medium bowl, combine flour, ground lavender buds, lemon zest, and salt.
In a large mixing bowl beat the butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar. Beat until combined. Beat in as much of the flour mixture as you can with the mixer. Stir in any remaining flour mixture.
On a lightly floured surface, roll dough into a 10-inch-long log. Wrap log in plastic wrap or waxed paper. Chill for 2 to 24 hours or until firm.
On a lightly floured surface, cut roll into 1/4-inch slices. Place slices 2 inches apart on prepared sheet pan.
Bake about 10 minutes or until edges are lightly browned. Transfer cookies to a wire rack and let cool.
Adapted from Better Homes & Gardens