Wrap the cooked lobsters belly-side up in aluminum foil with a bit of butter and place them on a baking sheet.
Heat the lobsters in the oven for 5 to 10 minutes until warmed through.
While the lobster heats, prepare the sauce by mixing 1/4 cup mayonnaise with finely chopped celery stalk, lemon zest (just the yellow part to avoid bitterness), juice from half a lemon, about 1/2 teaspoon dill (optional), a pinch of salt, and freshly ground black pepper.
Stir the sauce thoroughly until smooth.
Carefully unwrap the lobster from the foil after heating and remove the meat from the tail and claws using scissors or a meat hammer.
Toss the lobster meat gently in the prepared sauce.
Melt a generous amount of butter in a skillet and brush the brioche buns to soak up the butter.
Toast the buns in the skillet, flipping until both sides are golden brown.