Never lapped a set of precision machined and matched rings. Leupolds...Yep, several sets. But not machined rings.
The TPS TSR and Seekins Precision rings are what are called a "matched set". Which means they're machined at the same time on the same machine to the same tolerances, so as long as you buy a high-quality base (that's straight) and your mounting holes are straight, you shouldn't need to lap them. I've tested this by mounting just the empty rings up together on a base (and also on my Badger Dead-Level) and mic'd them with the calipers and found no reason to lap any of them.
Just my experience.