A chin implant is recommended when there is a recessive chin present. This will give more anterior projection to the mandible and will also help with jawline definition. Fatty deposits are located above and below the platysma muscle and a removed with surgery. A platysma plasty will also give more jawline definition once the sub-platysma fat has been removed.
From the photos you provide, it appears that you have a small chin and lower jaw. Anything that you do for the neck might be limited by this finding and, conversely, results would probably be improved by making your chin bigger, most likely with a chin implant. Any kind of liposuction (laser or otherwise) has its limitations but should be a bit helpful. Finally, depending on your skin laxity (and age), forms of neck "lifting" or tightening would likely be in order.
you have an 'underdeveloped lower jaw'. So a chin sliding genioplasty would help; but you would 'ideally' have a lower jaw advancement in order to best achieve the profile you want. Liposculpture is not a great idea since you primarily need a 'lengthening' of the distance from the throat to the chin point.