Preheat oven to 350°F and prepare baking pan with grease or parchment paper.
In a bowl, whisk flour, baking powder, baking soda, and salt until evenly mixed.
In a large bowl, beat butter, oil, and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Stir in key lime juice and lime zest until combined.
Add half of the dry ingredients and mix gently.
Pour in milk and mix again until smooth.
Add remaining dry ingredients and mix just until combined.
Pour batter into prepared pan and spread evenly.
Bake for 30 to 35 minutes or until a toothpick inserted in the center comes out clean.
Cool cake in pan, then transfer to a rack to cool completely.
Beat cream cheese and butter until smooth for frosting.
Add powdered sugar gradually and mix well.
Stir in lime juice and zest until frosting is creamy.
Spread frosting over cooled cake and garnish as desired.