Would fat transfer be the best option to get rid of the wrinkles under my eyes and crows feet? Lower face lift. (photo)

Frat grafting is an excellent procedure for filling in hollows or irregularities under the eyes, in the brow / upper lid junction, or any of the face that could benefit from additional fullness. When expertly administered the results can be smooth, natural looking and lasting. It is important to find a plastic surgeon with extensive experience and expertise in fat grafting. The proper placement of fat  is essential and it is critical that fat is never overfilled.  

Based on the photos provided. Your best option would be CO2 Laser treating the skin around the eyes and fat transfer to the upper cheek and lateral brow (temple region). See examples in link below. The fat transfer would restore youthful contour, just look at a portrait of yourself from your late teens or twenties. The laser would smooth and tighten the skin.