What type of nutritional supplementation can support healing after facelift? Can taking type 1 collagen with HA help?

You should try to eat a healthy balanced diet to promote healing. - fruits, veggies, fish.  Taking collagen and HA does nothing to promote or improve the collagen in the skin. Waste of money.  If you want take a multi-vitamin.  Some Omega-3 supplements are also good for skin hydration.    

There really is no benefit to any nutritional supplements and a healthy individual. Anything you take should be reported to your surgeon as some of these are biologically active and can actually create problems.

There is no need for any special diet - just a healthy well balanced diet (and this applies to all procedures).  Patients always ask these questions, and unless you are eating a really poor diet, not getting enough proteins or calories, and you are deficient on nutrients because you are malnourished, there is not much to alter in your diet.  In general, I recommend vitamin C and folic acid found in prenatal vitamins.  However also as a general rule, I recommend patients stop all non-prescription vitamins, supplements, herbals 2 weeks before surgery as some can cause increased bruising or bleeding during and after surgery.