Although it may be hard to "fix" the cake, one way to salvage what you have into a dessert is to make it into cake balls or cake pops! They aren't hard to make and depending on how much lime syrup you used, it would be easy to create the balls †o stick.
TO MAKE CAKE POPS:
Take your cake and with your hands, crumble the cake into the pan. Add frosting and in your case, more lime syrup, to make it a thick consistency. Then use a spoon and make even size balls out of your cake. Bake them for 9 minutes at 350 degrees or until they start to get hard. Then, Add popsicle sticks, skewer sticks or even plastic straws into the balls and drizzle them with your frosting(again lime syrup) and put them in the freezer to harden!!!
If you have extra time, please check out my question!