First things first...is your FL die a bushing model or one piece? If it is one piece. try decapping first, sizing without the expander and mandrel, and then lubing your necks and expanding them with a expanding die and mandrel that you would use to prepare for neck turning. I have tested this and it helps quite a bit.
On the thing about lock rings, multiple tests have shown some slight improvement in concentricity by placing an O ring under a conventional lock ring. That is the reason that Lee lock rings have O rings.
If your die is one that works with bushings, what is the fired diameter of your necks, and what is your bushing size. When the amount of reduction becomes too large, as it may be with a factory chamber, it can cause concentricity issues, and there may be better ways to size.