Hi,
Here is a link showing what I did to prepare and tune a lock that needed a lot of work like products from L&R, Davis, M&G, and Pedersoli. It shows a worse case scenario. Really good locks like Chambers, Caywood, Hollenbaugh, Kibler, and Laubach don't require much or any tuning work. Chambers locks usually just benefit from polishing the inside of the plate and any bearing surfaces on the tumbler, sear, bridle, and frizzen. The top of the frizzen spring is always worth polishing highly where the toe of the frizzen rubs against it. I always polish off any grainy texture from the casting process including casting seams inside and out on a lock regardless of maker. Leaving that cast finish is evidence of lazy or rushed work in my opinion. The thread below shows what I did to bring an L&R Queen Anne lock up to an acceptable standard for me. Portions of what I did may be all that is necessary with your lock.
https://americanlongrifles.org/forum/index.php?topic=60628.msg610320#msg610320
Keep in mind, some commercial locks can be really terrible. I just finished fixing two Pedersoli locks, a Lott and a Bess, that were nightmares of shoddy work. On the Bess I had to add a bronze bushing to the tumbler hole and drill it straight to correct a tumbler installed at an angle. They drilled a grossly oversized hole in the bridle so the angled tumbler would still fit in the hole. I had to fill that hole with welded steel and redrill it. On the Lott, the gap between the pan and frizzen was enough to spill out priming, the sear was mangling the lip of the half cock notch with every shot such that the lock no longer held at half cock, and worse, the sear bar dropped below the edge of the lock plate when in half cock and full. You cannot install a lock like that and have it work safely, yet some hack did and sold it. Tuning a lock really depends on the lock because manufacturing quality varies a lot by maker. I rarely work on other peoples lock's anymore except in special cases because that work is often so frustrating and I can never charge what I should to recoup my time. The lock in the thread above cost $170 but add to that at least $150 worth of work to bring it up to a standard just equal to a Chambers lock right out of the box, and then another $150 or so to make it into what I did. The Chambers lock at $200 is the real bargain.
dave