Can I sue if a Fort Lauderdale aviation accident that took the life of my loved one happened over international waters?

Yes. In that case, a federal law called the Death on the High Seas Act (DOHSA) gives your family the right to seek compensation for your pecuniary losses. It is a law that was originally written to address the death of sailors on ships at sea, but that courts have interpreted to apply as well to aviation accidents in international waters.