Rinse and peel jicama, then cut into 1/8- by 2-inch sticks.
Cut off and discard peel and white membrane from grapefruits and oranges. Working over a bowl to catch juices, cut between inner membranes and fruit to free segments, dropping fruit into bowl.
Pit, peel, and thinly slice avocados.
Line a platter or salad plates with lettuce. With a slotted spoon, lift fruit from bowl; reserve 2 tablespoons juice for persimmon dressing and the rest for other uses. Arrange fruit, avocados, onion, and jicama on lettuce.
Spoon about 1/4 cup of dressing over salad. Offer remaining dressing and salt to add to taste.