Remove and discard any stray bits of shell or cartilage from the lobster meat and cut it into large chunks (about ¾-inch). Sometimes, you'll see the claw meat left whole, placed across the top of the roll for an impressive presentation.
In a bowl, gently toss lobster with 3 tablespoons mayonnaise and celery (if using). The lobster should be lightly-coated, but not weighed down by the mayonnaise. Add an additional tablespoon of mayonnaise, if needed.
Taste the lobster salad. Some brands of mayo are a bit tangier than others. If the salad needs more brightness, add a squeeze of fresh lemon juice. Season to taste with salt and pepper.
Cover the lobster salad and refrigerate for 30 minutes, or up to 6-8 hours if prepping ahead.
To assemble the lobster rolls, preheat a griddle over medium heat. Butter the flat sides of the hotdog buns and grill for just a couple of minutes per side, until toasted.
Place lettuce (if using) onto each bun and mound with ¼ of the lobster salad. Serve with your favorite sides, such as coleslaw, dill pickles, french fries, or kettle chips.
