In a large bowl, cream together butter and sugar until very smooth, about 3-4 minutes. Beat in egg, and vanilla and lemon zest for another 2 minutes until combined well.
In a separate bowl, stir together the flour, baking powder, and salt. Add to the butter mixture a little at a time and mix just until combined. Do not over mix.
Cover, and chill dough for at least one hour (or overnight).
Preheat oven to 375 degrees F. Line cookies sheets with parchment paper.
Roll out dough on lightly floured surface 1/4 to 1/2 inch thick. Cut into shapes with cookie cutters of your choice. Dreidels, menorahs and Texas worked for me! Place cookies 1 inch apart on cookie sheets lined with parchment.
Bake 7 to 10 minutes until lightly brown on the edges. Cool completely before frosting.
To make royal icing, use an electric mixer to mix egg whites, cream of tartar and confectioners' sugar until stiff peaks form, adding water as needed, about 5 minutes. Color with food coloring if desired, put in piping bags, and use immediately. Cover icing with a damp towel when not using. Icing takes a few hours to dry completely so keep that in mind!