This grilled lobster is perfect for any occasion. Even if you don't have a lot of experience in grilling shellfish, this will be an easy recipe for you if you start with either fresh or frozen lobster tails. This recipe assumes you aren't starting with a live lobster. If you are, you will have the extra step of killing it by parboiling before you use the tail for grilling. To use frozen lobster tails, defrost them in the refrigerator before splitting and grilling them. Butter or olive oil? You have a choice to make, as you can use either. In fact, you may want to make two batches of the sauce in any case. One will be used to season the lobster while grilling, while a second batch can serve as a dipping sauce for your grilled lobster.