Some rings, especially the steel are machined well enough that lapping isn’t required. But I would lap the rings first. Burris usually puts in some friction paper in the package with their standard steel rings. My scope has never moved on me for about 5 years now. Shot it quite a bit. The Burris tactical rings aren’t going anywhere. Very wide with 6 screws per ring. There is a plastic collar inside the rings as well. I put those on my 34mm tube. Generally the (steel) rings stay in place if they are well degreased and lapped, with blue Loktite on the screw threads, torqued correctly. I have never used aluminum rings because I think aluminum is more likely to slip. But plenty of people use them without problems.
Sorry to dig up an old thread - but is carbon friction paste ever used for this type of application? I'm thinking of the stuff used in the bike industry to keep torque numbers low enough for carbon parts.
