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In a food processor or blender, blend the egg and lemon juice for 10 seconds. With the processor running, slowly pour in the oil through the feed tube and process until emulsified. Should the mixture become too thick, with the machine running add water 2t at a time. Add the tarragon, salt, and pepper, and pulse to blend. Transfer to an airtight container and refrigerate for at least 30 minutes before using. (The mayonnaise will keep tightly covered in the refrigerator for up to 24 hours.)Place eggs in medium bowl and add 1/4 cup of the mayonnaise, the shallots, garlic, and cayenne, and mash with a fork to blend. Ad the chopped lobster meat and the additional mayonnaise a little at a time to reach desired consistency. Adjust seasoning, to taste. Cover and refrigerate until ready to serve. In a large bowl, toss the mesclun with the olive oil, salt and pepper to taste. Arrange on a platter. With a sharp knife, cut each avocado half lengthwise almost all the way but not completely to the other end. Place each half seed side down on the lettuce and spread into a fan shape. Place the lobster-egg salad in the center of the 2 avocados and the asparagus spears around the sides of the plate. Top the avocados with a dollop of the mayonnaise, and a little caviar. Sprinkle with the tarragon and serve.
