Still can't blink or close eye after lower face lift, it been over a month - no improvement.

Opening and closing of the eyelids should not normally be affected from a lower face/neck lift.  Were there other procedures that were performed on your eyelids?  Without knowing the details of your surgery, it is impossible to know what might have caused the issue.  It is also impossible to know if there might be any permanent damage without having those surgical details.  

It is not clear from your description whether you had any eyelid surgery? It would be very hard to understand how could your eyelid problems be related to lower face lift surgery. Photos and in-person evaluation would help to clarify that problem. You should discuss your concerns and seek explanation from your surgeon. Eyelid massage helps as well as protective eye-drops and glasses. Good luck.

The temporal branch of the facial nerve on that side is most like the issue.  The more anterior of these branches supply the muscle around the eye.  In the recovery room after a facelift I ask patients to open and close their eyes to evaluate this branch.  I don't use long acting local anesthetics so I can do this more easily.  If the eyelid will move even slightly then I presume you have a neuropraxia.  This can result from swelling around the nerve or stretching of a nerve.  That is why other providers are asking for associated procedure like eyelid surgery or brow lifts.  If you are unhappy with your surgeon or want a second opinion then use the Smart Beauty Guide to locate another surgeon in your area.  Bring your operative report and photos with you.