Can laser treatment and fat grafting help minimize the appearance of genetic under eye hollows and pigmentation? (photos)

The hollowing can only be treated with addition of volume. Since you are interested in a permanent option, I think fat grafting is your best bet. As for the hyperpigmentation, this will be a lot harder to treat as this is more of a skin issue- if you haven't already tried some hydroquinone, I would start there. At the same time of when you get the fat grafting, you should also see if you can get some nanofat injected to help too. To some degree, though, the hyperpigmentation will always be present due to your skin type so make sure you have realistic expectations.

Dark under eye circles can make you look tired and older than you are. I would use a combination protocol that includes topical Melarase creams first, followed by a combination of injectable fillers, fractional laser, and RF to blend out the eyelid hollowness and tighten the skin.
Recommended Creams: Melarase Brightening Kit
MelaClenz
Melarase AM
Melarase PM
Melapads
Replenish Retinoid Cream
Best,
Dr. Karamanoukian
Realself100 Surgeon

This condition responds well to stem-cell enhanced fat transfer and pigment lasers like Aerolase, a laser that is good for all skin types.
The hollowing in younger people is genetically caused, and in older people, by the aging process, and the fat and bone resorption that accompanies it.
I have been impressed with the correction of pigmentation with fat grafting alone. You can also enhance the results, in terms of fat retention and pigment correction, with the addition of stromal vascular fraction. SVF is the component of fat that has a large number of stem cells. I currently use Lipocube to get SVF from the harvested fat and do the grafting with 1/3 SVF and 2/3 microfat under the orbital rim and cheek. Depending on the degree of hollowing or cheek volume augmentation needed, two treatments are done.
For patients who don't want a surgical procedure, like fat grafting, Renuva is an option. Renuva is an allograft matrix derived from acellular human tissue (nothing to reject), that when reconstituted with saline and injected into an area that already has fat cells, stimulates those far cells to multiply and enhance volume. Result are obtained over a 3-6 month period and a second treatment can be done if needed.
As an adjunct, depending on skin type, vascular and/or pigment lasers can help diminish the dark circle appearance.