Preheat oven to 350 degrees F (175 degrees C). Line 24 muffin cups with paper liners or spray with cooking spray.
Mix cake mix, water, eggs, and vegetable oil together in a bowl using an electric mixer until batter is smooth, about 2 minutes. Add 2 tablespoons lime zest, lime juice, and food coloring; mix well. Pour batter into the prepared muffin cups.
Bake in the preheated oven until golden and a toothpick inserted in the center of a cupcake comes out clean, about 18 minutes. Cool cupcakes on a wire rack.
Beat butter and cream cheese together in a bowl using an electric mixer until smooth and creamy. Add 2 tablespoons lime zest and vanilla extract to creamed butter mixture; mix well. Mix confectioners' sugar, 1/2 cup at a time, into creamed butter mixture until frosting is smooth; chill in refrigerator until frosting is thickened, about 30 minutes.
Spread frosting onto each cupcake and top with sprinkles.