What is this large indent causing a shadow below my lip? What can be done to fix this nuisance?

You have a short chin and an overlying deep labiomental fold. You are correct in that lower lip augmentation will magnify the deficiency of both. Ideally you need both chin and labiomental fold augmentation for maximal improvement.

 Hi, I have performed many facial shaping procedures using dermal fillers, silastic facial implants (cheek, chin), liposuction and/or facelifts for over 30 years.  From the photos, your cheeks are very flat in the front, the chin is quite weak and the lips are very thin.  These combine to create an elongated, oval shaped face.  
 Following my beauty principles, women look the most feminine, youthful and attractive with heart shaped faces.  Heart shaped faces have cheeks that are full and round in the front.  Cheek augmentation with a dermal filler or using silastic cheek implants (for a permanent enhancement) will create full, round cheeks that will feminize the entire face.
 I have performed many Chin Augmentations using chin implants for over 30 years.  From the photos, your chin is weak.  A weak chin creates an imbalance making the nose appear larger, the mid face top heavy and the lower face look short that de-emphasizes the lips and allows early formation of a double chin and "pseudo-jowls".   Pseudo jowls differ from "jowls" in what causes them, what they represent and how they are best treated.  Pseudo jowls are defined by a fold of tissue laxity that goes from the corners of the mouth to approximately 1/3 or 1/2 the distance to the lower jaw line.  It’s caused by a weak chin and its lack of tissue support around the chin and mouth area.  It's best treated by correcting of the weak chin with a silastic chin implant.  Jowls are described below in greater detail.  Chin augmentation using a chin implant will add projection to the chin creating harmony and balance to the lower face. 
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty.  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.
 The back portion of your jaw line is a bit weak and can be augmented, without making your face appear masculine, using precise placement of a dermal filler (I prefer using Restylane Lyft).   I have performed many lip augmentation procedures using dermal fillers or lip implants for over 30 years. From the photos, your upper lip is small compared to your lower. Following my beauty principles, the lips should be full with the upper lip approximately 75 % the size of the lower lip for the lips to appear balanced. The lips can be augmented using a dermal filler or a Permalip implant.
Dermal fillers and lip implants offer a much more reliable volume for augmentation of the lips than permanent fillers or fat injections which are associated with increased, unwanted, side effects.
Hope this helps.