Asymmetry in Lips and Eyes? (photo)

Yes I see a very obvious asymmetry. Best to compare to younger photos. If a recent occurrence than seek full work up and testing to check for a medical/nerve/genetic issues. 

You do demonstrate right upper eyelid ptosis.  It is hard to tell if the right eye is more sunken than the left.  A personal consultation to assess this question would provide an answer.  There is a well describe chronic sinus problem that can cause slow changes in the eye socket called silent sinus syndrome.  What happens is the sinus opening closes due to chronic sinus inflammation or trauma.  The negative pressure in the sinus slowly causes the boney orbital floor to bow down making it look like the eye is shrinking.  Do you have this?  You appearance is not really consistent with this but an examination look for what is called enophthalmus and appropriate imaging studies may be required to answer these questions.  I suggest you see an oculoplastic surgeon or a otolaryngologist to answer this question. 

After looking at your picutre upclose, I think you see a physician that can do some direct neurological nerve testing, if this has always been the case (looking at past photo's) then some difference can be addressed with injectables.