Nice video, I think the important takeaway is DOC and higher feed rate, when he increased the feed rate at the very end the surface finish improved.
I have thought about this. The DOC need not be spectacular, but it does need to be enough that the tool, with it's little un-sharp radius on the cutting edge will push far enough into the work so that the chip, forced into plastic deformation, will flow into the trick curves of the chip-breaker.
That by itself is not enough. If the feed rate is too slow, the tool will not be making a steady flow of new connected chip running into the breaker. This is where the "other" radius comes in to play, that being the tip radius. Here I am talking of turning along the spindle axis (Z?) rather than for facing. To get the metal to keep flowing into the chip breaker, the tool has to travel fast enough to, in effect, maintain that chip depth of cut while on the move, but in the Z-axis direction as well.
I guess this can be hard work for a small lathe, but it does not have to be done at blinding speed. The feed rate is locked to an increment advance "per revolution". Even when you get it OK in theory, it is possible to run into tool-tip buildup, sticking and tearing tiny streaky chunks out of the metal, depending on what type it is. I don't get too many chances to experiment here. Once I get an OK finish happening, I want to go on and get the part made. I guess I should time out with some scrap steel, and start trying the combinations, but I don't think I have enough life left.