In a medium bowl, whisk together avocado oil, lime juice, cilantro, salt and pepper.
Pour half of the mixture into a large ziplock bag with the shrimp. Close the bag and with your hands work the marinade to make sure all of the shrimp is covered by the marinade. Place in the refrigerator to marinate for at least 1-2 hours.
Pour the other half of the marinade mixture into a food processor or blender. Add 1/2 avocado to the food processor (about 1/3 cup diced). Blend until smooth. Optional: Add up to 1/4 cup water if you want to thin out your dressing (I did not). Leave in the refrigerator until ready to use.
When you are ready to cook the shrimp, preheat a medium sized skillet over medium heat with 1 tablespoon of oil.
Add the shrimp to the skillet. Cook for about 3 minutes on each side, until the shrimp is cooked through and pink in color.
Toss together the cut up lettuce, tomatoes, extra 1 1/2 diced avocado, and cooked shrimp.
Spoon avocado dressing over the salad and serve immediately.