Make the cookies: Preheat oven to 350 degrees. Beat butter, sugar, vanilla, and lemon zest and juice until combined. Beat in flour and 1/2 teaspoon salt. Wrap dough in plastic wrap, and refrigerate until firm, at least 2 hours.

Turn out dough onto a lightly floured surface, and roll out to a scant 1/4-inch thickness. Cut out about 18 cookies using 2 sizes of flower cookie cutters (one 3-inch and one 3 3/4-inch). Transfer to parchment-lined baking sheets, and refrigerate for 30 minutes.

Bake until edges just start to brown, 14 to 18 minutes. Let cool completely.

Decorate the cookies: Transfer each batch of tinted icing to a separate pastry bag fitted with a small round tip (you can use as many colors as desired). Pipe an outline of icing around the edges, then "flood" each cookie with more icing to cover. Immediately pipe a circle of small dots in the center of each cookie using a different-colored icing. Drag dots to outer edges using a toothpick to create thin lines. Repeat with remaining cookies and icing. Transfer cookies to parchment-lined baking sheets, and let dry completely, about 30 minutes.

Once cookies are set, pipe a large dot in the center of each cookie using the same tinted icing as the small dots. Gently sprinkle poppy seeds around large dot. Let dry completely.