I can tell you that Muller Rimfire barrels are hand lapped to 180 grit silicon carbide or 120 grit aluminum oxide. Paul is among the best in the world and the successes of muller barrels in the Rimfire BR world strongly reinforce that statement.
There is no arguing with facts and verified results. What is missing from the above is context:
The linear grain size of 180 grit crystals averages 0.003". That is taller than your typical .22 rimfire land to groove height of 0.002". Why is that not too rough in the instance of Muller Barrels? I am speculating, but I bet that their barrels are much harder than your typical mild steel airgun barrel. Of course, most of the grit height is imbedded into the lead lap, so it does not cut grooves into the barrel bore surface 0.003" deep.
For context, if you want to precision grind a fine finish into the taper in a lathe spindle, you do not use an 800 grit wheel; you use an 80 grit wheel.
Despite that seeming way too rough, you will battle to cut hardened steel with too fine a grit because too many grains will make contact with the work at one time. Too much contact area would require so much combined force to cut, that the tooling will spring excessively, making it difficult to reach the required specs on the finished part. It will also take "forever" to cut away the distortion in roundness that often occurs with quench hardening.
By using a coarse grinding wheel, proportionately fewer granules or grits make contact with the work at the same time. This enables cutting pressure to be reached at individual grains, without so much total force on the tooling as to spring it significantly.
Now, cutting mild steel with an 80 grit grinding wheel is likely to result in a rough looking surface, because it cuts so easily. For that, finishing wheels are required that have a much finer grit. But then precision tooling interfaces (such as a taper) are never made from mild steel.
It takes more energy to impart a fine finish to a hard steel surface, but far finer finishes are achievable that are also precise in shape, than for soft metals. You can buff soft metals to a mirror finish easily, but try to buff something to a precise shape.
So, while Paul Muller uses coarse grits to lap their rimfire barrels, with great success, I am going to propose that such coarse lapping is a "corner case" for airgun applications; rather than representative. of best practices. Airgun shooters regularly use JB compound, with improvements reported for consistent grouping, while making barrels easier to clean, when they eventually need it. I think this does not prove JB compound is best. It simply means that the people using it have a common experience. I would add that how any abrasive is used matters more than exactly which brand or grit.
A respected manufacturer who posts on GTA, fire laps all his new big bore air rifles with 360 grit valve lapping compound, much to the chagrin of those who like a mirror finish in their barrel bores. I like fire lapping for its effectiveness and simplicity. I also know that it should not be overdone, from experience.
Hard lead lapping is best, but not for those who have not learned how to do it properly. Also, it should be done on barrel blanks, so both ends can be cut off and thrown away. Hard lead Lapping a finished barrel is risky, so it should only be done if the barrel shoots poorly, because of reasons that cannot be fixed by less aggressive means. If you lap a finished barrel that shoots really well, you likely are not going to improve it. The opposite is more likely.
An exception to this, is if a PCPs barrel retention screws were over tightened, and have dinged the barrel all the way to bore. Then focused lapping to get rid of the tight spots might be indicated. The other exception is if the bore has several tight spots along its length from manufacturing, then lapping those out is likely to make the barrel shoot better. You can't harm a barrel that already shoots poorly. You just have to know when to stop. If you "improved" a barrel into oblivion, you were going to replace it anyway
. If you can shoot .22 pellets from your .177, you probably lapped too much
I think
"best grit size" for lapping barrel bores should be offered as a conditional statement. One that includes the steel the barrel is made of, its hardness before rifling and after rifling (hardness is method dependent). Also, if the coarse grit lap is followed by a finer one. I would like to ballpark discussion, then focus on specific details, in context. Else we might be arguing absolutes, using either pocket gophers, or pocket battleships as our reference.
As Thomas Air PCPs have a very good earned reputation, I would me more interested in how your barrels are made and prepared? I expect you to remain tight lipped, because that info is proprietary. If you are lapping them with 180 or 140 grit abrasive, I bet they are not made from mild steel.
Everything should be discussed in context. Arguing absolutes without context is silly, lazy or potentially deceptive.