What procedure can lift lateral cheek and correct hollow lower eyelid?

I find fillers work best in this area, and/or fat with PRP.  I suggest a formal consultation. There are skin tightening procedures as well that can be used , in place of surgery if you are a candidate for a non invasive approach.  Best, Dr. Emer.

Photos would have been helpful. But in general terms, before racing to invasive surgery, with its attendant expenses, greater downtime, and potential for scarring (however hidden), I would strong urge you to check out both "nonsurgical cheek augmentation" and "nonsurgical treatment of tear troughs and undereye hollows" using volumizing fillers in the archives of RealSelf.com or simply do an internet search using these key terms.  You will find that nonsurgically augmenting the cheeks not only can provide lift to the cheeks, but often secondarily improve the area immediately below the eyes. And even if some hollowness remains, this can equally be treated with injectable volumizers and fillers. The results are immediate, engender little to no downtime, and typically evoke a "Wow!" response right after treatment, which usually takes only about fifteen minutes in experienced hands.  In my Upper East Side Manhattan office, I typically use Voluma XC for augmentating the cheekbone region, Juvederm Ultra Plus XC (for the upper inner cheeks, if needed) and Belotero Balance for tear troughs. Not uncommonly, the Voluma XC cheekbone augmentation is all that is necessary. In my Israel satellite facility where a far greater number of regulatory agency approved fillers and volumizers are available, I would use Stylage XXL, Princess Volume and Teosyal Redensity II for each of these purposes, respectively.Make sure to consult with a board certified aesthetic physician before simply proceeding with surgery.

Neither option will correctly address the tear trough area.  For tear trough improvement, options include filler or fat injection, lower blepharoplasty, and tear trough implant. See an oculoplastic specialist.