In a shallow dish, combine lime juice, onion, 1 Tbsp. olive oil, ginger, 1/3 of the garlic, 1/8 tsp. salt, and 1/8 tsp. black pepper. Add steak, and turn to coat. Cover and marinate in the refrigerator for 1 to 4 hours, turning meat occasionally.
In a medium bowl, combine tomatoes, remaining 2 tsp. olive oil, 1/8 tsp. salt, and remaining 1/8 tsp. black pepper. Toss to coat. Thread tomatoes evenly on two 10- to 12-inch skewers, leaving 1/4 inch of space between tomatoes.
Preheat grill to medium. Remove steak from marinade. Grill steak over direct heat until the internal temperature reaches 150° (about 10 to 12 minutes for skirt steak or 15 to 17 minutes for flank steak). Grill tomatoes for 4 to 6 minutes, or until softened and browned. Remove steak and tomatoes from grill. Cover steak with aluminum foil, and let rest for 5 minutes.
Meanwhile, in a food processor or blender, combine cilantro, parsley, oregano, avocado oil, vinegar, red pepper flakes, remaining 1/8 tsp. salt, and remaining garlic. Process or blend until mixture is finely chopped but not completely smooth.
Thinly slice steak across the grain. Serve on plates with tomatoes. Spoon cilantro sauce evenly over all. If desired, serve with lettuce leaves.
