Preheat oven to 350 degrees Fahrenheit. Butter the sides and bottom of a 9x13-inch baking pan and lightly coat with flour. Shake excess flour off.
In a medium bowl, combine your dry ingredients: the flour with the baking powder, baking soda and salt.
Beat the butter in a stand mixer with the paddle attachment over medium speed until very creamy and soft, at least 2 or 3 minutes. Incorporate the sugar, continue beating until well mixed. Add the eggs, one at a time, and continue beating until they are all incorporated.
Reduce speed to low, and add a cup of your dry ingredients, then add the lime zest and juice. Continue adding the rest of the flour, and finally add the milk. Scrape the sides of the bowl with a spatula if need be, and continue beating the mix until it is spongy, fluffy and very well mixed.
Pour the batter into the prepared pan and bake in the oven for 50 minutes, or until the pound cake is puffed up, golden brown on top, and a toothpick comes out clean and moist, but not wet.
Remove from the oven. Let cool and serve. It keeps very well covered for up to a week.