Shred the rotisserie chicken into bite-sized pieces, discarding skin and bones.
In a large bowl, whisk together mayonnaise, sour cream, lemon juice, lemon zest, Dijon mustard, salt, and pepper until smooth.
Add the shredded chicken, celery, red onion, parsley, and dill to the bowl. Fold gently until everything is evenly coated.
Taste and adjust seasoning with more salt, pepper, or lemon juice if needed.
If using nuts, fold them in just before serving to maintain crunch.
Cover and refrigerate for at least 30 minutes to let flavors meld before serving.