Preheat oven to 400 °F for a convection oven, and to 425 °F for a regular oven.
Line two baking sheets with parchment paper of Silpat baking mats and set aside.
Mix lemon zest with granulated sugar and set aside.
Unfold the puff pastry dough. Roll out the dough to an even thickness with a rolling pin. Place the dough on a large cutting board.
Brush the dough(s) with the melted butter and sprinkle the lemon sugar over the melted butter.
Cut the dough into strips about 1-inch in width. Place the cut strips on the prepared baking sheet, twisting the dough two or three times while placing it down on the sheet.
Bake 13 to 15 minutes or until golden brown.
While the puff pastry bakes, make the icing. Combine icing ingredients (powdered sugar, butter, and lemon juice) and mix well.
Allow lemon puff pastry sticks to cool a bit, and drizzle with lemon icing.
Serve warm or at room temperature.Makes about 13-17 sticks, depending on how many ounces your dough is.If you use Pepperidge Farm brand puff pastry, there will be two sheets of dough. Use both sheets for this recipe, dividing the melted butter and lemon sugar evenly between the two sheets.