Is mesotherapy effective for eyelid area?

It all depends the goal of your treatment, messotherapy is a great option when you choose the right combination of treatments for the area you want to improve, there are some medications working in making your skin tighter, lighter color, with less wrinkles and hydrate your skin, if those are your main goals, it can be injected all around the area. Don't forget to go with an aesthetic expert physician to improve the results and avoid complications. 

Dr Luis Salazar 
Aesthetic Solutions 

Yes, mesotherapy is safe. But you need to do it with a well trained aesthetic physician as they are aware of the danger zones that need to be avoided. The amount of session you need usually depends on how severe your case is.
Your condition might be caused by multiple factors like volume-less, skin thinning and other reasons so combination treatment usually gives the best result.