Re-using Used Lifters on Another Cam

That's just a flat face. Automotive lifters have a crown so they spin in the bores.
That tool has a radius adjustment on it...several different radius are used depending on the lifter application. The stone is fixed but the arbor angle is adjustable. The lifter resurfacer I used in the 60's was part of our valve grinder and was on the backside of the bench...run by one motor via a belt drive.

Here's another video from a different shop.