After slugging a pistol barrel, what is the proper size bullet,(LRN)? Should it be the same as the measurements of the slug, or .001 over?

Ruger LC9

.001 over is usually best.

If you are shooting it out of a Ruger LC9, (Got that from your signature) it doesn't matter; that ain't a match gun. Any bullet you can get to chamber will work at 10 feet. Now, if you are shooting a well tuned match pistol, that is another story, and for a revolver, another one. Oops, I see you are asking about lead (alloy) bullets; you never want to shoot an undersized lead bullet; it will gas cut and lead your barrel no matter how hard it is. Bigger is always better with lead bullets.