As a general shop term,"lapping" is the process of cutting a harder material with grit that embeds in a softer material.That is not a book definition,but I have done considerable lapping in industry.
Often lead,copper,or brass are chosen as the softer material.
Generally,it is desirable for the lap to conform to the geometry of the workpiece.The very best you can do is cut off the high spots of irregularities,reduce the rms of the finish..the altitude difference between the high spots and the low spots.
Another benefit of barrel lapping is getting the "lay" of the surface finish ,the "grain" in loose terms,all going in the direction of the bullet.
You can imagine as a drill or reamer goes through,the marks are pretty much perpendicular to the path of the bullet,like washboard road or file teeth.
The barrel maker generally strives to keep the features of the rifling crisp,as cut,not rounded and washed out.And,it is desirable that the dimensions of the bore are uniform to slightly tapered ,the size reducing from breech to muzzle by a very small amount.Tight spots can be relived via lapping.
I do not know what method is used by modern barrel makers.I tried a method described in the book "Modern Gunsmithing" by Baker,IIRC.
A tapered brass wood screw is fixed to the end of a one piece cleaning rod.A patch is placed on the screw so lead can be cast around the screw inside the bore.This is all inserted from the breech,so the screw just protrudes from the muzzle.Then molten lead is poued in from the muzzle around the screw.The patch plugs it from falling through.
Space limits me from describing the whole process,but from this point on,the lap is not removed from the bore.As it is cast in place,it conforms to the geometry of the bore.Screwing the tapered screw into the lap tightens the lap.
Grit and oil are charged on the lap as it is partially,but never completely,protruded from the barrel.
Generally,the barrel maker is a whole lot better at it than an amateur effort.Generally,ameteur efforts subtract from the life/quality of a barrel ,rather than improve it.
IMO,the time to try lapping is when you figure you have nothing to lose.
Then relax,have fun,see what happens.
Fire lapping is one process an amateur can try.It involves firing bullets embedded with grit.
The bullet is formed to the shape of the bore in the throat,and does cut the "lay" all in the direction of travel.
I did it one time,with very good success on a "bargain" barrel.It was a 2 1/2 MOA metal fouler,with visible reamer and button gall marks at the muzzle.
I used cast lead 30-30 bullets charged with #9 diamond mold polishing paste.I fired about 20.This was a 30-06.After this treatment..this rifle became one of the more accurate in my possession.I won't say MOA,because you probably would not believe me.
Besides,I don't have scientific MOA evaluation for it,but "minute of 250 yd prairie dog" is close.
Now,there is one more activity that some may consider "lapping",but it is not.
That would be using some patch,mop,brush,etc charged with grit in the bore.IMO,the methods are nothing but detructive.Remember,the goal is to increase uniformity,decrease the RMS ,(high to low spot "altitude" change) by knocking off high spots.You cannot do this if your lap does not have its own form.A mop cuts the valleys at the same time it cuts the peaks,and it rounds and washes out the rifling form.It also does nothing to dimensionally uniform the barrel.
Its your barrel,but,IMO,abrasive with brush,mop,or patch is a misguided amateur effort by a person with high hopes.You may well find benchrest shooters that recommend it,but you are unlikely to find a quality barrelmaker that will recommend it.