Lipo and Dermabrasion for Fatty Lump Between Lower Lip and Chin?

This is an unusual area for a fatty tumor. Therefore it is unlikely that liposuction would be of any benefit. However, it is also a bad area for a scar and likely to develop thick scarring. So there is no easy answer.

It's difficult to determine the best procedure without actually feeling the area.  However, if it's soft you could try liposuction and save actual excision as a last resort.  Dermabrasion may not be necessary if liposuction does the trick.  Good luck!

The best answer comes from an evaluation in person. This way the physician feels the texture and gets an impression of its hardness, mobility vs. fixed position, its origin such as the epidermis or deeper structures. Resurfacing might make you lose enough epidermis that the texture will become shiny and smooth and you may lose pigment in that area (temporarily or permanently). An excision will replace that lump with a linear scar. It’s important to know what possibly caused this, how long it has been there and if it is growing.

I would need more information before I could offer an answer. Questions like how long has it been there? Is it getting bigger? etc.
My feeling is that liposuction in that area is not going to achieve what you are looking for. Based on the photo alone, without further information my inclination would be to excise the area.

Although the plastic surgeon was in the best position to give you advice, since he examined you, I would make a couple of comments about his recommendations.
First, I think that doing liposuction in this confined area of the chin is difficult, and achieving a smooth contour would be difficult through that approach.
Second, incisions in this area of the chin can heal very well. I have not had any difficulty with this area of the chin in terms of unsightly scars.
Having said that, I would also say that if liposuction is done and the results are not satisfactory, surgery would still be an option.