Cream together the butter, sugar and salt in a mixer fitted with the paddle attachment, until pale and fluffy, about 2 minutes. Add egg, beat until well blended, about 1 minute, then add vanilla and lemon. Scrape down the sides of the bowl.
Add flour, and baking powder, mix on a low speed until just combined. Gather dough into a ball, divide in half. Form each half into a flattened disk and wrap in plastic, chill for at least 4 hours. (I only chilled mine for 2 hours and it seemed to roll out and bake beautifully) It can be made up to 3 days ahead or freeze for later.
Preheat oven to 325°F. Line 2 baking sheets with parchment paper.
Working with one disk at a time, roll out dough between two sheets of wax paper or on lightly floured counter to 1/8″ thin.
Using decorative cookie cutters, cut out cookies and transfer to a cookie sheet, spacing 1 inch apart. Gather any scraps, roll them out until all the dough is used. If not using icing then decorated with sprinkles before baking.
Bake one sheet at a time until cookies are firm and golden around the edges, about 10 minutes for smaller cookies and up to 14 minutes for larger ones. Cool completely on rack.