Using an electric mixer, beat the butter and sugar until creamy and smooth, about two minutes. Add the lemon juice, zest and vanilla and beat well.
In a bowl, combine the flour, poppy seeds, and salt. Add the dry ingredients to the butter mixture and mix until combined. Form the dough into a disk and, wrap in plastic wrap and chill for at least 3 hours and up to 3 days or freeze for up to 2 months.
Preheat oven to 300° F. Roll the dough between two sheets of wax paper to a 1/4-inch-thick rectangle. return dough to refrigerator for an additional 30 minutes. Cut the shortbread into shapes with a two-inch cookie cutter, or use a knife, and place 1 inch apart on parchment-lined baking sheets. Do not reroll scraps, if using cookie cutter. Prick shortbread with a fork and bake until pale golden all over, 23 to 25 minutes. Cool on a wire rack.