Preheat grill to medium. Combine olive oil, juice of 3 limes, 4 garlic cloves and 1 tsp cumin in a shallow bowl or pie plate. Then add fish to this marinade and let it soak up the flavors for 15 minutes at room temperature, turning once after about 7 minutes. While fish is marinating, in a separate small mixing bowl, stir together the remaining lime juice, garlic and cumin with diced avocado, onion, jalapenos, and cilantro. Place marinated fish on hot grill and cook for approximately 5 minutes, turn and grill for approximately 5 more minutes, until opaque throughout. Place cooked fish on a cutting board, let it cook slightly, then slice into thin strips. While grill is still hot, place tortillas directly on it and grill them for about 30 seconds on each side. Place two tortillas on each plate. Put a lettuce leaf in each tortilla, fill with a portion of grilled, sliced fish, and top with tangy avocado salsa. Fold the tortillas over. Serve, and enjoy!
