How to Make It
Set up a very large ice bath. In a large pot of boiling water, cook the lobsters until they turn bright red but are not cooked through, about 6 minutes. Drain well and transfer to the ice bath to cool. Drain well.
Twist the bodies from the lobster 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 knuckles and remove the meat. Cut all the lobster meat into chunks and transfer to a bowl.
In a medium saucepan, melt 1 stick of the butter with 2 tablespoons of water over moderate heat. Transfer the mixture to a blender. With the machine on, gradually add the remaining cold butter until emulsified. Return the butter to the saucepan and warm over medium heat, then season generously with salt and pepper. Add the lobster meat and cook over moderately low heat, stirring occasionally, until just cooked through, about 5 minutes.
Meanwhile, in a small bowl, whisk the mayonnaise with the Dijon, mustard powder, 1 teaspoon of the lemon juice and 1 1/2 teaspoons of water. Season the mustard-mayo sauce with salt and pepper.
Using a slotted spoon, transfer the lobster to a medium bowl. Stir in the remaining 1 tablespoon of lemon juice and season with salt and pepper.
Brush the toasted rolls with softened butter and fill with the lettuce leaves and the warm lobster. Garnish with snipped chives, drizzle with the mustard-mayo sauce and serve right away with lemon wedges.