1. In a small saucepan over low heat, cook the butter with the garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper until the butter is melted. Set aside.
2. Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
3. Place a lobster on a cutting board, shell side down. Insert the tip of a large, sharp knife into the lobster’s body just below the head (no need to be shy about this process—it takes some strength), and cut the lobster open down the center, cutting through the body but not through the back shell. (The shell will hold the juices as it cooks.) Remove and discard the head sac and intestines. Rinse the lobster under cold running water. To help the lobster stay flat on the grill, insert a bamboo skewer through the tail meat. Remove the rubber bands on the claws. Brush the inside of the lobster with some of the butter. Repeat with the remaining lobsters.
4. Brush the cooking grates clean. Grill the lobsters, shell side down, over direct medium heat, with the lid closed as much as possible, until the tail meat is firm and white, 10 to 15 minutes, brushing occasionally with additional butter. (Soft-shell lobsters will cook more quickly than hard-shell lobsters.) At the same time, if your grill is big enough, grill the corn. If not, grill the corn after the lobsters. Brush the corn with some of the butter and grill over direct medium heat, with the lid closed as much as possible, until browned in spots and tender, 10 to 15 minutes, turning occasionally. Season the corn with salt and pepper.
5. Transfer the lobsters and corn to a large platter. Heat the butter mixture over medium heat until it comes to a simmer. Add the parsley. Serve the lobsters with the corn and the remaining butter mixture.