Joe_S,

  I'll admit my way is probably not the best way, but I've done many of them this way, and even made a few up from scratch.  I just get a piece of rod (mandrel) that's near the size of the hole, and cut a slit in it to take a piece of emery cloth. Chuck your die up in the lathe, and wrap a piece of emery cloth around your mandrel that will be a slightly tight fit and put in your tail stock. Be sure you wrap it the right way.  Be sure and start the mandrel in from the top side, as that's tapered and running the mandrel in tends to widen that slightly if you try it from the other end. With the lathe on run the mandrel back and forth slowly, going all the way thru, and as evenly as possible.

  Since you only want to take out .002" be sure and check the inner diam. frequently. It won't take long and you don't want to over do it.

  Be sure to measure the diam. of the hole before you start and only take out the amount necessary. You might find, after trying it out, that you might have to take out a little more.

  This is about the easiest way, short of a regular hone, to do this and the results have always worked out ok for me with a very nice smooth finish. Sometimes even better than when it was new.

  I wouldn't recommend taking out more than .003" or so. If you do things seem to get out of round after that.

PETE

I've done it with 320 grit wet-or-dry paper on a mandrel, used wet with cutting oil.  I've also found that opening a sizing die more than about .001" requires that a new push rod be turned to keep lube from leaking out around it.  (What did Lyman call that thingus?)  You want a "snug" slip fit.

David
Montezuma, IA

I'll throw in my two cents...

I've never lapped a lubrisizer die, but have lapped the body and/or necks of some sizing dies.. a couple that the neck of the die was grossly undersizing the neck, making more work for the sizing button.

I used the split mandrel (or just a split piece of wood) in the tailstock with wet/dry wrapped around it.
I keep it in motion, back and forth, as the die spins, and start "roughing" with 320 grit paper.  After a few minutes, I drive a lead slug through to check my size (easier to measure an OUTSIDE diameter of the slug then get something that deep in the die...).
When I'm within .001", I switch to 400 grit paper.
I start the 400 dry, and after a minute or two of lapping, I add some WD-40 and then keep it lubed.
That makes for slower cuttting action (the paper does load up), but also makes a better finish, and I'd rather sneak up on the dimension I need than blow past it!
Making holes bigger is way easier than makin' 'em smaller again.

And if you DO need to lap out more than a couple or three thousandths, you really need to concentrate on keeping your strokes with the mandrel EVEN and not "tipping" the mandrel and making a bell-mouth shape. 

Hope this helps!
Paul F.