Remove tail, knuckle, and claw meat from the lobsters and cut into 1/2-inch chunks. You should have about 1 pound of lobster meat. Refrigerate until chilled.
Drain lobster meat, discarding any liquid. Gently toss lobster with 3 tablespoons mayonnaise and celery (if using). The lobster should be coated, but not weighed down by the mayonnaise. Add an additional tablespoon of mayonnaise, if needed.
Taste the lobster salad. Some brands of mayo have more tang than others. If the salad needs more brightness, add a squeeze of fresh lemon juice. Season to taste with salt (if needed) and pepper.
Cover the lobster salad and refrigerate for 30 minutes, or up to 6-8 hours.
When ready to serve, preheat a griddle over medium heat. Butter the sides of the hotdog buns and grill 1-2 minutes on each side, until toasted.
Place a leaf of lettuce (if using) into each griddled hotdog bun and mound each with 1/4 of the lobster salad. Serve immediately with french fries, kettle chips, coleslaw, and dill pickles, if desired.