Preheat your oven to 350°F (175°C) to ensure even baking.
In a large mixing bowl, beat the eggs with sugar until light and fluffy. Gradually add flour and baking powder, mixing until just combined. Fold in lime juice.
Divide batter between greased cake pans and bake for 25-30 minutes until a toothpick comes out clean. Allow to cool in pans for 10 minutes.
Prepare the soaking syrup by dissolving sugar in warm water, then let it cool.
For the frosting, beat cream cheese and sugar until smooth, then mix in sour cream, lime juice, and zest until creamy.
Level the cooled cake layers if necessary. Brush one layer with soaking syrup, spread frosting, and sprinkle with coconut. Repeat with the second layer and frost the top and sides.
Garnish with remaining coconut and chill for at least an hour before serving.
