The lettuce sandwich is the salad sandwich reduced to its limit: a single leaf and nothing else. Crisp lettuce goes on buttered white bread, often with a smear of salad cream, and that is the entire build. There is no protein, no second vegetable, no cheese. The defining fact is that this is a sandwich with nothing to hide behind, made from what is in the house when there is almost nothing in the house, and its quality is decided entirely by the leaf and the moisture around it. It is not a poor relation of the salad sandwich so much as the austere extreme of it, the point past which there is nothing left to remove and still call it a sandwich.
The craft is keeping it from going limp and wet, which is harder than the short ingredient list suggests because there is no fat or salt doing structural work for you. The lettuce has to be cold and dry, washed and shaken or patted so it does not weep into the bread, and a crisp variety is chosen because a soft leaf collapses to nothing under the top slice and leaves only damp bread. Butter spread to the edges is the barrier that waterproofs the crumb and, with its salt, is most of what makes the sandwich taste of anything at all. Salad cream, when it goes in, is applied in a measured stripe rather than a flood: enough to season the leaf and add a tang, not enough to soak the bread or drown the only thing the sandwich contains. The leaf is left whole or torn large so it holds a structure and gives a real crunch rather than shredding into wet ribbons.
The variations are the point at which something is added back and it becomes a different, fuller sandwich. A slice of tomato brings sweetness and its own bleed. Cucumber adds a second water-crisp note. Egg or cold ham puts a protein against the leaf and turns it into a proper salad build. Each of those crosses out of this sandwich's deliberate austerity and deserves its own article rather than being crowded in here.