Preheat oven to 350 degrees F (175 degrees C). Grease 2 large baking sheets. Stir together the flour, baking powder, salt, 1/2 teaspoon nutmeg, and 1/2 teaspoon cinnamon in a bowl; set aside. Stir together 1/3 cup sugar, 1/4 teaspoon nutmeg, and 1/4 teaspoon cinnamon in a separate bowl and set aside.
Cream together the butter, 1 cup sugar, and lime zest in a large bowl until light and fluffy. Gradually beat in the lime juice, then the flour mixture 1/2 cup at a time. Form the dough into walnut-sized balls, and roll in the spiced sugar mixture. Arrange onto prepared baking sheets 1 inch apart. Flatten the balls slightly using a decorative cookie stamp or the bottom of a glass.
Bake the cookies in the preheated oven until the edges of the cookies turn golden brown, 13 to 16 minutes. Cool the cookies on wire racks, then store in an airtight container up to 1 week.