Build your salad on a large platter. Use bib lettuce as the bed, then layer the tomatoes and scatter the red onions around the platter.
Cut the avocado in half lengthwise cutting around the pit. Separate the halves and scoop out the pit with a spoon, then use the spoon to scoop the avocado from its skin. Place the avocado in a food processor bowl and combine with lemon juice, chopped red onion, cilantro, coarse salt and water. Grind until the avocado mixture is smooth, then stream oil into dressing. Adjust seasonings and pour over salad, then serve. Dressing may be stored 3 or 4 days in airtight container.