Based on the photo of the coating being lapped off, that ring is no more than .001"-.002" out of round, referenced to the lapping bar, with a slight low point. That dimension corresponds to one fourth or one half the thickness of a sheet of printer paper. It looks more like a cant issue because axial alignment is correct but the coating removed is pitched. Perhaps the issue is compounded due to the "rail" it's mounted on. It doesn't appear to be a true picatinny as the manufacturer took liberties with the mil-spec, and it's a picatinny mounted on a receiver, stacking tolerances.
I don't know if anyone here has taken measuring instruments and measured how far off the rings might be before lapping away because anodizing coatings are very thin, and steel coatings like black oxide are vanishingly thin, 0.00005" thick. A thickness of 0.00005" corresponds to a sheet of paper being split thickness-wise 80 times.
If people are making such a big fuss about lapping rings, has anyone ever tried to centerless grind their scope tubes into roundness? Has anyone taken a precision micrometer and measured the OD of their scope tube? Has anyone ever measured the ID of their scope rings? By lapping material from the rings, you're fitting the rings to the lapping bar. You aren't fitting the rings to the scope tube. To precision-fit two mating surfaces together, you do it with Prussian Blue and make repeated markings, knock off the transferred high points, and repeat until you get as many bearing points as you require.
Has anyone taken the time to measure the TIR of their scope tubes at the two points where rings will be mounted? Your scope body roundness is probably ovoid by .0005". The tube probably tapers in diameter from one end to the other, and TIR will register a measurable figure given that long, skinny tubes of aluminum are not perfectly round and will have an off-axis bend to them
Maybe it's time I market a scope tube grinding kit. I have no doubt that not all rings line up perfectly, but attacking the rings is only half the equation, if folks are that bent on getting a perfect fit. As mentioned by another poster above, you can remove too much material and ensure an incorrect fit once you introduce the stresses of the cap screws clamping down on the scope tube.