Prepare a gas grill for direct-heat cooking over medium heat; see Grilling Procedure .
Plunge 2 lobsters headfirst into a large pot of salted boiling water and cook, partially covered, over medium-high heat 8 minutes (for 1 1/4-pounds lobsters) to 9 minutes (for 1 1/2-pounds lobsters) from time they enter water. Transfer with tongs to an ice bath and let stand until completely cooled. Return water to a boil and cook and cool remaining 2 lobsters. Remove meat from claws, joints, and tails. Coarsely chop meat.
Whisk together lemon juice, oil, and 1/2 tsp salt in a large bowl. Whisk in scallions, celery, celery leaves, and parsley, then add lobster and gently toss. Season with salt.
Melt butter with garlic in a small saucepan over low heat, mashing garlic with a spoon.
Brush inside of buns with garlic butter. Grill, buttered side down, until golden, about 1 minute.
Fill buns with lobster.
Cooks' notes: Lobsters can be cooked 1 day ahead. Remove meat from shells and chill. Buns can be grilled in a lightly oiled hot 2-burner grill pan over medium heat or toasted in a 350ºF oven 5 to 7 minutes.