Combine oil, lemon juice, soy sauce, scallion, garlic and ground ginger in bowl. Toss 1/3 of the marinade with the tofu to coat and marinate in refrigerator for 6 hours.
In a large bowl, combine the mushrooms, tomatoes, red pepper and onion. Pour remaining marinade over vegetables and toss.
Thread the tofu and vegetables, alternately on skewers.
Cook on the grill 10-15 minutes, brush with marinade and turn several times.