Stir together preserved lemon rind, 2 tbsp. lemon juice, and the oil in a small bowl. Season with salt, pepper, and more lemon juice if needed.
Slice celery stalks very thinly on the diagonal, using a mandoline or sharp knife. Cut fennel bulbs in half lengthwise; cut out and discard cores. Thinly slice crosswise. Pit dates and cut into slivers. Combine with celery, fennel, and parsley in a large bowl.