Combine the celery, chicken, salt, and pepper in a large mixing bowl.
Put-in the lime juice and mayonnaise. Fold the mixture to mix all the ingredients.
Arrange 2 leaf lettuces over the tortilla wrap.
Scoop half of the chicken mixture on top of the lettuce. Fold the opposite sides of the tortilla and roll starting from the end of the unfolded side until the chicken salad is completely secured.