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Crack the lobster, remove all the meat, cut it into large chunks and set aside. (Lobster shells can be kept to make a delicious soup.)
Mix the mayonnaise with the lemon juice, celery, cayenne and a small pinch of salt, then fold the lobster through to combine. Taste and adjust the seasoning. If eating straight away, leave at room temperature – or chill for up to 1 day in advance.
To serve, split the rolls and lightly butter on all sides, including the outside. Heat a griddle pan and griddle the rolls in batches on all sides. Divide the lobster mix between the rolls, scatter with chives (if using) and serve on a platter with napkins, a bowl of crisps and some gherkins.