In a large mixing bowl, combine mayonnaise, lemon juice, and Dijon mustard. Whisk until smooth and creamy.

Gently add crab meat and chopped celery to the dressing. Fold together carefully to maintain the crab's texture.

Cover with plastic wrap or transfer to an airtight container and chill in the refrigerator for at least 30 minutes.

Taste the crab salad and adjust seasoning as needed before serving.

Serve on a bed of lettuce or with crackers, garnished with parsley and lemon wedges.