Mix celery, olives, and 1/3 cup mayonnaise. Gently mix in crab. Add salt, pepper, and lemon juice to taste.
Drain artichokes and save marinade. If artichoke hearts are whole, cut lengthwise into halves or quarters.
Place a lettuce leaf on each plate and lay a slice of tomato on the lettuce. Mound crab mixture equally onto tomato slices and arrange artichokes beside tomatoes. Drizzle salads lightly with artichoke marinade.
If desired, top crab mixture with a small dollop of mayonnaise. Dust salads lightly with paprika.