Mikecr,
The die is restrained on the up stroke by its threads in the press, not the lock ring, that only serves to hold the dies rotational position relative to the press. Using and O ring under the lock ring, or a Lee lock ring allows the die and press threads to align true to each other. With a metal to metal fit between the lock ring, and the top of the press, the die can be locked down slightly cocked. I have a lot of experience doing it both ways. The only down side to the Lee lock rings is that it is easy to move the ring on the die when removing the die from the press. I have solved this by putting a split lock ring above the Lee, setting the die, and then snugging the split lock ring down onto the top of the Lee ring (shile being careful not to move it on the die) and then tightening the screw so that it is jammed into position against the Lee ring, and both rings on the die. I use this with an index mark for a starting point for fine adjustment of the die, and set up so that I have a little O ring compression (giving rotational position stability) at the highest point of adjustment that will be used (for new brass). Since brass hardens as it is repeatedly fired and sized the FL die must be reset as this happens to maintain the desired amount of shoulder bump. With the proper setup, the entire range adjustments can be done with one lock ring setting (with an O ring), without the Lee ring going metal to metal on the top of the press. Because I work with more than one set of brass, that have different amounts of work hardening, I reset my FL die for each lot, and at the beginning of each loading session, using my index mark as my starting point. It only takes a few tries on the first couple of cases to set the die, and by resetting it each time, I avoid accidentally using a hard brass setting on new brass, and having too much bump.
Obviously, to maintain consistency of work hardening, within any given set of brass, I fire and size in rotation, running through the cases to the end, and then starting over at the beginning.
I check my brass for consistency of bump and concentricity. Switching to the Lee lock ring has slightly improved the concentricity, and has not changed the consistency of the bump, so there is no disadvantage, and there is some advantage.
The other things that have given me straighter sized brass and straighter ammunition, are switching to a carbide neck bushing (more dimensionally correct) and switching arbor press seaters, to one that has a much closer fit on the case.
Because my loaded ammo had runout (on the bullet) that was less than .002 before I made these changes, the amount of improvement that could reasonably be expected was small. But each of the three things that I have described has made a contribution to improving the average concentricity of my loads.