Sprinkle the cucumber with salt and let drain in a colander for 20 minutes. Rinse and pat dry.
In a bowl, whisk together the vinegar, sugar, oil, chiles, and ginger. Add the cucumber, papaya, and cilantro and toss. Line a serving platter or 4 individual plates with lettuce leaves, and top each with about 1/2 cup of salad.
Yield: 4 to 6 servings