Heat oven to 350°F.  Combine flour, baking powder, baking soda, and salt in a medium bowl and whisk to combine.

Combine shortening and sugar in the bowl of a stand mixer and beat on medium speed until fluffy, about 3 to 4 minutes. Add eggs one at a time, letting the first incorporate fully before adding the next. Stop mixer and scrape down the sides of the bowl. Add lime zest and juice and beat until smooth.

Add flour mixture to the mixing bowl. Start mixer on low, then gradually increase speed until completely incorporated. Add cranberries and continue mixing until incorporated.

Scoop into tablespoon-sized mounds and place on an ungreased baking sheet, about an inch apart. Bake until golden brown on the bottom, about 12-15 minutes.