The Connecticut lobster roll is defined by a refusal: no mayonnaise, no celery, no lemon, nothing cold. Warm lobster meat is tossed in drawn butter and piled into a griddled split-top bun, and that is the entire sandwich. The decision to serve it hot is the whole identity. Butter does the work mayonnaise does in the Maine style, binding and enriching, but it does it warm and clean, so the sweetness of the claw and knuckle meat is the loudest thing in the sandwich rather than a dressing built around it.
The craft is in restraint and in the bun. The lobster is cooked, picked into large pieces, and warmed gently in butter rather than reheated hard, because overcooked meat goes to rubber and the sandwich has nowhere to hide it. The split-top frankfurter roll is the structural reason the format works at all: its flat sides are griddled in butter into a crisp gold wall on each face while the crumb stays soft, so a wet, heavy, structureless filling has a spine that holds for the length of the sandwich. Butter on the meat and butter on the bread are the same idea applied twice. Served too slow, the warm meat steams the toasted faces back to softness and the roll collapses into a buttered salad, so this is a sandwich built to be handed over and eaten immediately.
The variations are mostly the argument the Connecticut style exists to take a side in. The Maine cold roll dresses the meat in mayonnaise with a little celery and lemon and serves it chilled, the same catch read in the opposite direction. The broader New England seafood roll runs the same buttered split-top under fried clams, scallops, oysters, or a Rhode Island stuffie, swapping the lobster for whatever the boat brought in. Each of those is a codified build with its own logic and its own defenders, and each deserves its own article rather than being crowded in here.