Heat a gas grill to medium-high or the coals in a charcoal grill to medium-hot.
Combine mayonnaise, sour cream, vinegar, lemon juice, scallions, parsley, chives, 1/8 teaspoon of the salt and the pepper in a medium bowl.
Lightly coat grill rack with oil or nonstick cooking spray. Season tuna with remaining salt and 7 teaspoons of the lemon pepper. Grill about 3 minutes per side for medium. Meanwhile, season tomato halves with remaining 1 teaspoon lemon pepper and grill, cut-side down, about 5 minutes, until slightly charred.
Toss greens with 6 tablespoons of the dressing. Serve with tuna, tomato halves and remaining dressing.