Combine avocado, garlic, mayo, mustard, agave nectar, herbs, lemon juice, salt and pepper in a food processor/blender and puree until smooth. Add 1/2-1 tablespoon water to get the texture of a thick sauce.
Pour sauce over chicken and stir to incorporate evenly. Add walnuts. Refrigerate, covered, for at least 1 hour for best taste.
Place a heaping 1/4 cup in center of each piece of Bibb Lettuce. Wrap and serve.