Begin by cooking the lobster: Fill a large pot with enough water to cover the lobsters and bring to a boil. Add the lobsters to the pot, cover, and cook for 8-10 minutes or until fully cooked. Remove the lobsters from the pot and let cool.
Once the lobsters are cool, remove the meat from the shells and chop into bite-sized pieces.
In a mixing bowl, whisk together the mayonnaise, celery, lemon juice, and parsley until well combined. Season with salt and pepper to taste.
Add the chopped lobster meat to the bowl and gently toss with the dressing until well coated.
Melt the butter in a small skillet over medium heat.
Toast the hot dog rolls in the skillet until lightly browned on each side.
To serve, divide the lobster mixture evenly among the toasted rolls and enjoy!