After a traumatic tooth extraction, does bone regrow or shrink during healing process in lower jaws?

Yes. Most teeth require bone grafting. The reason you can get away without it is if you have thick bone on the outside of the tooth & the tooth socket(s) are very small.  The mandibular molar is one of these cases.  The doctor can see the size of the socket after extraction. Not grafting is a risk not worth taking as the bone shrinks fast & may require a graft later on.  It has been proven that graft then implant vs graft & implant has less bone loss around the implant afterwards.  Hope this helped.

bone graft is not necessary. but we always advice bone graft, because by that we are increasing chances of maintaining bone height and width. without bone graft, suppose results in bone resorption, augmentation procedure is required which is very expensive.

Bone grafting isn't absolutely necessary but it is highly recommended. Bone grafting in an extraction site helps keep the bony ridge from collapsing. If you choose not to have grafting done you may limit your choices if implants or create a situation where the surgeon has to place an implant in a less favorable position. In the long term bone grafting is worth the added up front expense.