Alternative Options to Facelift for Patient with Heart Condition?

Your eye anatomy is difficult to treat without surgery.
However, you can achieve some improvement with the use of fillers, botulinum toxin (i.e., Dysport), chemical peels, laser resurfacing, radiofrequency or IPL treatments. It would be best for you to meet with a professional to discuss these options. IF you are on blood thinners (including aspirin) you run the risk of bleeding. You should discuss the possibility of having to discontinue these medications with your cardiologist prior to treatment.

I have operated on many people with minor heart problems as well as people who have had angioplasties, stents and even cardiac bypass surgery. However, these people have all been relatively healthy at the time of my surgery and they have all been cleared by their physicians (usually cardiologists).
In general, the biggest potential problem with facelift surgery is not the surgery but the anesthesia. Facelift surgery can be performed with local anesthesia as well. A mini lift type procedure with local anesthesia may work well in your case. The use of tumescent local anesthesia employs very little lidocaine and only a scant amount of epinephrine.
If surgical procedures are truly contraindicated in your case because of a severe heart problem, consideration can be given for the use of filler injections for creases and depressions, BOTOX® for forehead furrows and crows feet, non-invasive (or minimally invasive) laser, peel or other resurfacing type procedures for improving the quality of the surface of your skin.