Dawg gone: I started lapping rings several years ago, and won't mount any scope without it,now. You won't believe how little of your scope ring is actually coming in contact with the scope, it has to cause pressure points and misalignment. Can I give any quantifiable evidence of improved accuracy? NO. But when I do have a problem with accuracy on a gun, I can rule out ring misalignment automaticaly. I guess in some ways it's peace of mind, you pay too much money for your scopes, to just clamp them up in a vise.
Now, if your on a budget, let me tell you I did. Go to your local machine supply shop or do a search on line for "drill rod". You can buy a 3'piece for about 12-15$ it will normally have a diameter tolerance of about .001" per foot of length. Which I think is good enough. Then stop buy your local automotive machine shop, it will have to be one of the old timer places, that still does actual engine work. And see if they have valve lapping compound, if not you can probably find it on line also. Most containers will have 1/2 "fine" and 1/2 "coarse" in the same container. Now for less than 20 bucks you have a lapping tool that you can really get a hold of, and which you can also use to twist in scope rings. And sometimes it can come in very handy when lining up windage adustable rings. Sorry this post ran so long, hope some of what I said, is helpful.