In a large mixing bowl, combine the mayonnaise, Dijon mustard, lemon juice, and Old Bay seasoning. Mix until smooth.
Gently fold in the lump crab meat, diced celery, diced red bell pepper, and chopped green onions. Be careful not to break up the crab meat too much.
Season with salt and pepper to taste. Adjust the seasoning if necessary.
Cover the bowl with plastic wrap and refrigerate for at least 30 minutes to allow the flavors to meld.
Before serving, give the salad a gentle stir and garnish with chopped parsley if desired.