The Maine lobster roll is defined by a piece of bread engineered specifically for it. The split-top frankfurter roll has flat, crustless sides cut so it can be laid on a griddle and toasted in butter into a crisp gold wall on each face, while the interior stays soft. That toasted exterior against a tender inside is the whole reason the format exists, because the filling brings no structure of its own and the roll has to be the spine. What makes this the Maine version specifically is the dressing, or rather the near-absence of it: chilled lobster meat, a thin bind of mayonnaise, a little celery and lemon, served cold. The restraint is the recipe.
The craft is a few decisions made precisely and then left alone. The lobster meat, claw and knuckle and tail, is cooked, chilled, and dressed only enough to hold together: too much mayonnaise and it becomes lobster salad in a bun, too little acid and lemon and it reads flat. The split-top roll is griddled in butter rather than toasted in a slot, because the butter caramelizes the cut faces into a surface that holds up against a cool, slightly wet filling for the length of the sandwich. The contrast is the point: warm, crisp, buttered bread against cold, barely-dressed lobster. Get either side wrong, under-toast the roll or over-dress the meat, and the sandwich collapses. A New England seafood shack lives on doing exactly this and nothing more, fast, all afternoon, off a flat-top.
The variations are mostly a single regional argument. The Connecticut roll runs the same buttered split-top but serves the lobster warm, dressed with nothing but drawn butter, and that cold-mayonnaise-versus-warm-butter divide travels with the eater rather than the recipe. Beyond it, the same split-top frame carries the clam roll with fried whole-belly clams, the fried scallop roll, the oyster roll, and the Rhode Island stuffie, each doing the trick with whatever the boat brought in. Those are real sandwiches with their own rules and deserve proper articles of their own rather than being crowded in here.