Stir together the mayonnaise, celery, dill, chives, lemon juice and salt in a large bowl.
Add the shrimp to the bowl and gently stir to combine.
Heat a large cast-iron skillet over medium heat. Spread both sides of the buns lightly with mayonnaise.
Toast the buns in batches until golden, about 2 minutes per side.
Lay the lettuce leaves inside the toasted buns, then fill with the shrimp salad. Garnish with more dill and serve with chips.
