Combine the flour, baking powder, and salt in a bowl and set aside.
Put the butter and sugar in a large bowl or 64-ounce Pyrex cup. Beat with an electric mixer on medium-high until smooth, about 2 minutes. Add the eggs and beat until fluffy, 2 to 3 minutes. Add the lemon juice and vanilla. Reduce speed to low and slowly add the flour mixture. Mix until just incorporated.
Divide the dough in half and flatten each portion into a 1-inch-thick disk. Wrap in plastic and refrigerate for at least 1 hour.
Heat oven to 350° F. Roll out the dough on a lightly floured surface to 1/4 inch thick. Cut into desired shapes and place on a parchment-lined baking sheet. Scraps can be combined and rolled out again. Bake 10 to 15 minutes or until light golden brown.