Strategies for management of volume deficiency near the lower lids would include fillers or surgery. Conventional facelift affords access to the area. A midface lift breaches the connective tissue barrier between the lower lids and cheek. It's careful reestablishment is necessary to prevent lower eyelid position problems. Make certain you understand this.
There are so many variables here, and no pictures, so it is hard to comment. If you are hollow, then you will need either fat transposition which is usually done from inside the lid, or fat transfer. Some surgeons like to do a midface lift through the lower lid. YOu have to be very careful that this is done correctly or you could get an ectropion post-op. Get a couple of opinions before you do anything. See an oculoplastic surgeon since they specialize in the lids.