Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Set fish aside.
For pesto, in a blender or food processor combine the parsley, cilantro, cheese, nuts, garlic, the 2 teaspoons lemon juice, and the 1/8 teaspoon salt. Cover and blend or process with several on-off turns until nearly smooth, stopping the machine and scraping down sides as necessary. With the machine running slowly, gradually add the 2 tablespoons oil; blend or process until the consistency of softened butter, scraping sides as necessary. Transfer to a small bowl. Set aside.
In a small bowl stir together the 1 tablespoon lemon juice and the 2 teaspoons oil. Brush fish with lemon mixture. Sprinkle fish with salt and pepper.
Place fish in a greased grill basket, tucking under any thin edges. For a charcoal grill, grill fish on the rack of an uncovered grill directly over medium coals until fish flakes easily with a fork (allow 4 to 6 minutes per 1/2-inch thickness of fish), turning basket once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place fish on grill rack over heat. Cover and grill as above.) To serve, spoon pesto over fish and top with tomato. Makes 4 servings.