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Combine butter, parsley, chile flakes, garlic, lemon zest, salt, and pepper in a bowl; set aside. Using a cleaver, split lobster in half lengthwise through its head and tail. Scoop out and discard the yellow-green tomalley and break off claws. Transfer lobster halves, shell side down, to a baking sheet; crack claws and place them on the baking sheet. Drizzle halves and claws with oil, and season with salt and pepper.
Heat a charcoal grill or set a gas grill to high; bank coals or turn off burner on one side (see "Grilling 101"). Place lobster halves, flesh side down, and claws on hottest part of grill; cook until slightly charred, 2-3 minutes. Flip lobster over and using a spoon, spread lobster with the garlic-parsley butter; continue grilling until lobster meat is tender, 3-5 minutes more.
While steaming and boiling may be the most common methods, grilling whole lobster is a surprisingly easy way to cook the popular crustacean. A quick cleaver through the body kills the lobster instantly and painlessly. (To preserve its freshness, this step should be done immediately before cooking.). If serving grilled lobster as a main course, count on at least one, 1-pound lobster per person (though you can get away with less if you’re also grilling an assortment of other seafood). And don’t ditch the precious shells when you’re finished! Instead, freeze and then use them to make a rich lobster stock, which is the perfect base for bisque and other seafood soups and sauces.
