Facelifts in my practice are often done on heavy set women who i remove fat from the neck and face when I perform the facelift. Skinny women there is no issue. If a great deal of weight is lost more then 20% of current weight, there will probably be a consequence of a need for a secondary procedure if the result is unacceptable to you.
A small degree of weight loss may not have much effect but drastic weight loss is likely to result in loss of facial volume with a resulting degree of skin laxity. It is unclear from your question whether you have had a facelift already or whether you are contemplating a facelift since you may be in the process of losing weight. In the ideal world, in order to maintain a good result from facelift surgery, it is best to defer surgery until you have lost weight. Weight loss in the face can be quite ageing due to the loss of volume. In these situations of hollowness in the face fat transfer combined with a facelift often provides the best results.