Mix the flour and sugar on a work surface. Cut the cold butter into pieces and spread around the flour. Add the lemon zest and knead into a smooth dough. Wrap in plastic and chill for 30 minutes.
Preheat the oven to 180°C (approximately 350°F). Line two baking sheets with parchment paper.
Roll out the dough until about 3 mm (approximately 1/5 inch) thick on a lightly floured surface. Use cookie cutters to cut out stars. Place the cookies on the baking sheets. Bake for 8-12 minutes. Remove and cool on a wire rack.
Mix the lemon juice and powdered sugar into a thick icing. Pour into a pastry bag and decorate the cookies, or use a brush to ice the cookies. Let dry and serve.