Your goals should determine the scale you use.
If you really want to be less than 0.1 grain uncertainty, then you will not be using the Lyman or the RCBS.
None of these inexpensive strain gage load cell scales are going to perform at the 0.1 grain uncertainty level.
We don't need to swirl over the scale debates in your thread, so if I just stick to the capability expectations....
Lots of things can cause abnormal problems with electronic scales. Static, EMI/RFI, temperature swings and breezes, vibrations, etc.
But then lets stick to what is normal capability. If the environment is causing your scale to freak out, then you will need to test it in a better place that is stable in temp and quiet in terms of electrical noise.
To learn what your two units can actually do, you will need a spread of check weights across the total range. Make sure you have at least one near max and half range as the minimum. More data points across the range is better.
You check the values of those after allowing the scale to stabilize in temperature for at least a half hour, and then check the null and gain, which is the zero and the cal weight. Then take all those additional values.
Run that test on five samples of each weight including your zero for a session, then run several sessions over time, say for example different days.
That data will show you what your scales can really do. Circle back if you want help with the math on that data. You probably get the idea, that each point will have dispersion and that the steps will also show the linearity of the scale.
I find it is always comforting to have a check weight value very close to the charge weights you use the most. Things can and do fail with electronics, and by keeping an eye on those check values, you can catch problems early.
Good Luck.