Step 1With a food processor running, drop the lavender through the tube. Add sugar and lemon zest, and pulse until combined, then add flour and salt and pulse.
Step 2Add butter and pulse until just incorporated. Continue pulsing while adding the lemon juice through the tube, just until dough forms a ball.
Step 3 Roll the ball into a log about 10 inches long, wrap in plastic and chill for at least 1 hour. (Dough can be frozen for up to 1 month — slightly thaw before cutting and baking.)
Step 4Heat the oven to 350 degrees. Slice the log crosswise into one-half-inch slices and arrange on an ungreased baking sheet, spacing the cookies about 2 inches apart. Bake until the edges are golden brown, 20 to 25 minutes. Cool the cookies on a rack.