In a 6- to 8-inch frying pan over medium heat, stir or shake nuts until golden, 3 to 5 minutes. Pour from pan and let cool.
Cut peel and white membrane from oranges and grapefruit. Over a bowl, cut between membranes to release fruit segments; put in bowl.
Peel, pit, and slice the avocados; coat slices with some of the citrus juice from the bowl.
Line a large platter with lettuce leaves. Arrange oranges, grapefruit, avocados, papaya, and grapes on leaves. Sprinkle with nuts. Moisten with a little of the poppy seed dressing, then spoon portions of salad onto plates and add more dressing and salt and pepper to taste.