Preheat the oven to 325℉ and lightly grease a large cookie sheet.
Beat the butter and sugar together on medium-high speed until well-blended. Then add the lime juice and mix again until it's incorporated, about 30 seconds.
Whisk all the dry ingredients (flour, baking powder, salt, and lime zest) together in a separate bowl.
Slowly add the dry ingredients to the wet, just until everything comes together to form a workable dough.
Divide the dough into 12 small pieces, and shape into balls about 1" across. If the dough sticks to your hands, refrigerate it for 10-15 minutes. Space the balls 2" apart on your cookie sheet. You can refrigerate the entire pan again for 10 minutes if you feel they're too sticky or warm.
Bake for 12-15 minutes. Pull them out when they are lightly colored. These will not get very dark. Depending on your pan, you may want to gently lift them and check the bottoms after 13-14 minutes to ensure they're not burning. If the bottoms are dark, pull them out.
Gently transfer the cookies to a wire rack. They will be very soft, but will solidify as they cool.