Place butter, sugar, and orange zest in a large bowl and beat with an electric mixer until smooth, about 5 minutes.
In a separate bowl, combine flour, baking powder, baking soda, ginger, nutmeg, allspice, cinnamon, cloves, and salt. Set aside.
In a separate bowl, whisk the eggs, molasses, and lemon juice together. Set aside.
Add the dry ingredients to the butter and sugar mixture and combine. Add the egg mixture and combine. Remove the dough from the bowl and split in half. Wrap each half of the dough in plastic wrap and refrigerate for 15 minutes.
Preheat oven to 350 degrees.
Lightly flour a flat surface. Use a floured rolling pin to roll the first half of the dough until about 1/4 inch thick. Lightly flour cookie cutters and cut out the shapes. Use a metal spatula to transfer to a lightly greased baking sheet. Repeat process for remainder of dough and second half. Bake until browned around the edges, about 8-10 minutes, rotating the trays halfway through. Remove from oven and transfer cookies to cooling rack.