Preheat the oven to 300°. In a large pot of boiling water, cook the lobsters until they turn bright red, 8 minutes. Drain and let cool.
Twist the bodies from the tails. Using scissors, cut along the underside of the shells and remove the meat. Halve the tails lengthwise and discard the dark intestines. Crack the claws and remove the meat in one piece. Remove the knuckle meat. Transfer the lobster to a bowl and refrigerate until chilled.
Holding a lime leaf, pull off the stem to divide the leaf in half. Repeat with the remaining leaves. Rub the leaves with oil; transfer to a baking sheet. Bake for 8 minutes, until crisp.
In a small skillet, heat the 1 tablespoon of oil. Add the shallot and cook over moderately low heat until softened, 2 minutes. Mash the anchovies with the shallot. Add the curry powder and cook until fragrant, 1 minute. Scrape the mixture into a bowl and let cool. Stir in the mayonnaise, lime juice and dill and season with salt. Refrigerate for 15 minutes.
Fold the curry mayonnaise into the lobster. Spoon the salad into the buns; top with the lime leaves and cucumber.