Cook and cool the lobster, remove the meat, chop into ¼-inch chunks, and place in fridge until assembling croque monsieurs. Slice the Gruyère thinly with a peeler or mandolin. Lay out 4 slices of bread, place a layer of Gruyère on bread, a layer of lobster, lemon zest and chives, another layer of Gruyère, and finish with the remaining 4 slices of bread.

Preheat a nonstick pan on medium heat. Spread softened butter onto outsides of sandwiches and place in preheated pan. Cook for 2–4 minutes, flip and cook for 1–2 minutes; remove from heat. The bread should be lightly golden brown but not dark. Slice sandwiches into diagonal pieces and serve as is, or top with a poached or fried egg to make a croque madame.