The lobster sandwich is the plainer reading of lobster between bread, and what defines it is restraint rather than the enriched roll. Fresh picked lobster meat goes on good sliced bread with butter or a light bound dressing, a squeeze of lemon, and almost nothing else. There is no sweet brioche carrier and no heavy sauce. The discipline is to get out of the way of an expensive, delicate shellfish and let it be the whole statement, which is why a lobster sandwich made with the morning's catch needs so little and a poor one cannot be rescued by what is piled on it. This is the sandwich at its most honest about the ingredient: bread, butter, lemon, lobster, in that order of how much they matter.
The craft is the handling of the meat and the moisture around it. Lobster is sweet, firm, and easily ruined: it is cut into generous pieces and either left barely dressed or turned through just enough mayonnaise to hold, never beaten smooth, because the clean flake is the texture that separates lobster from paste. Lemon is applied as a squeeze rather than folded in, so it lifts the sweetness without slackening the bind or weeping into the bread. The bread is plain and good, white or brown, sliced rather than rolled so it presses flat and holds the pieces in an even layer instead of letting them shift, and butter on the crumb is the only lubrication where no mayonnaise is used, bridging the meat to the wheat and sealing the bread against the lobster's moisture. The bread stays plain on purpose because a good lobster is loud enough alone and an assertive loaf only masks it.
The variations are a short list of what is set against the meat. A light mayonnaise and lemon bind turns it into the dressed reading. A turn of cucumber adds a cold, water-crisp counter to the richness. A few chopped chives through the bind add a single mild onion note. The soft enriched-roll treatment and the wider coastal shellfish shelf of crab and crayfish are each the same restraint met in a different format or catch and deserve their own articles rather than being crowded in here.