Preparation Combine lemon juice, anchovies, shallot, vinegar, and garlic in processor. Blend until shallot and garlic are finely chopped. Add avocado, sour cream, parsley, tarragon, and basil; blend until almost smooth. With machine running, add olive oil through feed tube in thin stream. Transfer dip to small bowl. Season to taste with salt and pepper. DO AHEAD: Can be made 1 day ahead. Cover and chill. Place bowl of dip on large platter. Surround with shrimp and vegetables.
Preparation Combine lemon juice, anchovies, shallot, vinegar, and garlic in processor. Blend until shallot and garlic are finely chopped. Add avocado, sour cream, parsley, tarragon, and basil; blend until almost smooth. With machine running, add olive oil through feed tube in thin stream. Transfer dip to small bowl. Season to taste with salt and pepper. DO AHEAD: Can be made 1 day ahead. Cover and chill. Place bowl of dip on large platter. Surround with shrimp and vegetables.