Boil 2 cups of water in a medium saucepan. Add the rice and salt and return to a boil, stirring once or twice. Reduce the heat to low and simmer, covered, stirring twice to promote stickiness, until all the moisture is absorbed, about 18 minutes. Allow to cool, uncovered, for about 15 minutes, or remove to a plate to speed cooling.

Combine the vinegar, scallions, horseradish, 1 1/2 teaspoons of the lime juice, and the soy sauce in a small bowl. Stir into the rice. Toss the avocado and remaining 1/2 teaspoon lime juice together in a separate small bowl.

To assemble: With a long end of a lavash half facing you, lay a quarter of the rice mixture evenly over the lavash, leaving a 1-inch border. Distribute a quarter of the crab, avocado, and ginger slices evenly over the rice and roll away from you, as tightly as possible. Complete the wraps with the remaining ingredients. Or, if you prefer, prepare all at once assembly-line style. Slice in half on the bias if serving for lunch. For appetizers, cut into 1- to 2-inch pieces and serve with the spirals facing up.