Here is my lapping tool adventure. I had to bring some 5mm (~0.197")O1 drill rod down slightly to an acceptable fit & finish. Its an idler gear axle for the radial engine I'm building. The OD of the lap is 5/16", basically to match a nominal drill size. The smaller hole is a stress relief & springyness guestimate. My plan was to kind of keep the same basic design & grow progressively larger series of tools for larger laps maintaining a similar dimension of the lap annulus thickness. Too thick & its hard to compress & get a feel. Too thin & its fussy to machine.
The lap is 6061 aluminum. I don't have copper & the idea was I would test this aluminum against brass & CI. I made simple slits in the lap ID with the scroll saw but forgot to put a fine metal jewler blade in there so its not the best. I tried to maintain a rougher OD finish to help with grip, but now I think that's completely unnecessary. The interesting thing about drill rod (at least the stuff I'm buying), is that it looks shiny & dimensionally quite accurate, but when you first touch the lap to it with least amount of pressure, you can actually feel some 'oblong-ness'. I pre-blued it with a felt pen to try & take a pic hopefully showing rubbed off hills, but the ink itself washed off. Anyway, after a few strokes which I think also conditions the lap, it feels constant. Just a matter of increasing pressure, clean, check, repeat. I bought a set of Aliexpress diamond lapping paste tubes & took a guess at the grit. It is quite creamy but a drop of oil makes it slide a bit better on finishing.