Is there a way to make the bottom lip also project forward a bit more when doing a chin implant?

 A chin implant is inserted through sub mental approach to give forward projection to the chin and mandible. There is also small amount of added vertical height and lateral width that occurs with the implant as well. The implant will have no effect on the lower lip.

A chin implant will not significantly change the lower lip projection. This would only occur with orthognathic surgery and lower jaw advancement for correction of malocclusion if present. Donald R. Nunn MD Atlanta Plastic Surgeon

A chin implant will improve chin projection and contour but will have no effect on lip projection. However the lip can be improved by injecting or placing one of many different materials at the same time.

The chin implant will not make your bottom lip project forward.  The purpose of the chin implant is to project the chin forward.  Yes, you can have a bit of filler in  your lip at the time of surgery, or you can have a lip implant.  I use Alloderm implants and the results are very natural and beautiful.