Peel and chop the avocados and place them in a medium bowl. Sprinkle 1 tablespoon lime juice over the top and set aside. Reserve the remaining lime juice for later.
In the bowl of a food processor, combine the mayonnaise, sour cream, parsley, garlic, about one-quarter of the diced avocado (reserve remaining avocado for later), the remaining lime juice, and a little salt and pepper. Blend until smooth. Set aside.
To a large bowl, add 3 ½ cups chicken, bacon, onion, remaining chopped avocado, and the dressing, and gently fold the mixture together. Fold in the remaining ½ cup chicken, if needed, to reach the desired level of creaminess. Season with additional salt and pepper, if desired.
Serve on sandwich rolls, on toasted whole wheat bread, or roll it into wraps.