Preheat the oven to 350°F. Line a 12-cup muffin pan with cupcake liners.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large mixing bowl, beat the butter, oil, and sugar until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract, lime zest, and sour cream until smooth.
Add the dry ingredients and mix just until combined. Do not overmix.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full.
Bake for 18 to 20 minutes, or until a toothpick inserted into the center comes out clean.
Let the cupcakes cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.