In a mixer set with the paddle attachment, beat the butter over medium speed until soft and creamy, about 5 minutes. Add the granulated sugar and continue to beat until well mixed and creamy, another 2 to 3 minutes. Beat in the egg yolks, add the lime zest and continue to beat until fully incorporated, another 2 minutes or so. Reduce the speed to low, and gently add the all-purpose flour, salt and baking powder. Continue to beat for another couple minutes. The batter should be completely homogeneous and feel a bit dense and heavy.
Transfer the batter to a large mixing bowl. Rinse the bowl of the mixer well and change the paddle attachment to the whisk attachment. Beat the egg whites on medium-high speed, until they hold stiff peaks, about 4 to 5 minutes. Slowly, incorporate a bit of the fluffed-up egg whites into the heavy batter. Repeat with the rest of the whites, folding them gently but persistently, until the batter is completely incorporated and seems lighter and fluffier. Don’t over mix, or you will remove the puff effect form the beaten egg whites!
Preheat the oven to 350°F. Butter the sides and bottom of a loaf pan and lightly coat with all-purpose flour. Shake out any extra flour.
Pour the batter into the prepared mold and bake in the oven about 50 minutes, or until the pound cake is golden brown on top, seems beautifully fluffy and a toothpick comes out clean. Remove from the oven. Let cool for at least 10 minutes.