If your chicken isn't already cooked, poach 1 lb of chicken breasts in simmering salted water for 12–15 minutes until they reach 165°F (74°C), then cool and dice. Dice or shred the cooked chicken into small, even ½-inch pieces and place in a large mixing bowl. Even pieces mean even flavor in every bite.
In a small bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, salt, and black pepper until smooth and creamy. Taste it now — it should be tangy, lightly salty, and bright.
Pour the dressing over the chicken. Add the diced celery, red onion, and chopped dill. Fold gently with a spatula until every piece of chicken is coated — don't mash or overmix.
Cover and refrigerate for at least 30 minutes. This rest lets the flavors meld — the onion mellows, the dill perfumes the dressing, and the whole filling tastes noticeably better.
Split the croissants and toast them cut-side down in a dry skillet over medium heat for 1–2 minutes until golden and warm. Lay a lettuce leaf on each bottom half, then pile on a generous scoop of the chilled chicken salad, about ¾ cup per sandwich. Cap with the top half.
Serve immediately with dill pickle spears and kettle chips on the side for the full deli experience.