Light a grill. Bring a large pot of water to a boil and fill a large bowl with ice water. Plunge the lobster into the boiling water head first and cook for 2 minutes. Using tongs, transfer the lobster to the ice water to cool; drain and pat dry. Place the lobster on a work surface and, using kitchen shears, cut down the center of the underside from tail to head to break through the shell. Using a heavy knife and a kitchen mallet, cut the body in half. Remove both claws.

Set the lobster, cut side up, on a rimmed baking sheet and add the razor clams. Drizzle with 2 tablespoons of the olive oil and 1 tablespoon of the vinegar. Grill the lobster claws, turning occasionally, for 5 minutes. Add the lobster halves, cut side up, and the razor clams to the grill. Cover and grill over high heat until the lobster meat is almost opaque and the clams are beginning to open, about 3 minutes. Turn the lobster halves and claws and continue grilling until the lobster meat is lightly charred and cooked through and the razor clams are open and the juices are bubbling, about 5 minutes longer.

Transfer the lobster and clams to a platter and drizzle with the remaining 2 tablespoons of olive oil and 1 tablespoon of vinegar. Season with salt and garnish with the parsley. Serve with lemon wedges.