In a blender or small food processor, combine scallions, vinegar, oil, ginger root, celery, water, sugar, soy sauce, ketchup, lemon juice, and salt. Puree until blended, about 1 minute.
In a large serving bowl, combine lettuce, cabbage, tomato, carrot, and cucumber. Pour the dressing on top and toss gently to mix. Serve immediately.
Tip: Most Japanese steak houses serve some version of this salad as a first course. The spicy-sweet ginger dressing is what makes it so good.