You are quite hollow here - we call it a deep superior sulcus. You can put some HA filler or some fat into this area which will help it appear less hollow. The browlift will make it look more hollow.
Not sure if you need a brow lift but to answer your question, you can have filler or fat injection in the upper eyelids/brows to make the area more full and more youthful.
Brow lift and deep eye sockets. The photo u showed is a naturally hooded eye. A brow lift will help the brows and a more alert look BUT the hollows will show more. Restalyne can be used with the brow lift for the socket and is reversible whereas fat is not.
If you have hollow deep eye sockets, they will be accentuated by elevating the brow with a brow lift.
You may want to consider a fat transfer to the brow region to add fullness to the lower brow. This can give the effect of adding and making it appear raised. At the same time there will be less hollowness to the upper eye region. Visit with a skilled Facial Plastic, Plastic or Occuloplastic surgeon to discuss your options. To test out the result you could also have an HA filler placed which is an non permanent option. If you like the result then follow up with fat grafting once the filler dissolves.
From the photographs it is apparent that brow lifting would accentuate the natural hollowness above your eyes. It also appears as if you may have some degree of eyelid ptosis . The best way to determine which procedures or combination of procedures (brow lifting, volume replacement and possibly ptosis repair) would be to be examined by a surgeon who is highly experienced in this area. As you live in LA, there are several excellent surgeons in your general geographic region. Best of luck!
Fillers, such as Juvederm Ultra Plus XC, can be used to treat hollowness under the eyebrows with gratifying results. It only takes about five minutes per side to reinflate area and the results are immediate.
The areas around the eyes are tricky areas to treat, so be sure to seek consultation and treatment by a board certified core aesthetic physician with experience and expertise in treating this region.