Combine tomatoes, celery stalks, onion, lemon juice, bay leaf, salt, and paprika in a large, heavy saucepan. Cover and cook over medium heat 15 minutes. Strain mixture, reserving tomato juice and discarding vegetables and bay leaf. Return tomato juice to saucepan.
Dissolve gelatin in 1/2 cup vegetable cocktail juice, stirring well. Add gelatin mixture to tomato juice in saucepan. Add additional vegetable cocktail juice to yield 4 cups. Chill until mixture reaches the consistency of unbeaten egg whites.
Fold in artichoke hearts, water chestnuts, egg, celery, green pepper, and olives. Pour mixture evenly into 8 lightly oiled 1/2-cup heart-shaped molds. Refrigerate until firm.
Unmold aspics onto individual lettuce-lined salad plates; garnish each with a dollop of mayonnaise.