Two interesting Lithgows serial number-wise.
I have two Lithgows in my collection of which neither are anything out of the ordinary save one thing: they are both very close to the beginning or end serial number range of the 1922 change from the MkIII* to the MkIII, then the subsequent 1941 change back to MkIII* production. The first, a MkIII* serial # B5806 was built in 1923 and was only serial numbered 100 away from the end of MkIII* production (A97165 to B5906). The second Lithgow, a No1 MkIII produced in 1941 serial # B64738 is only a few hundred into the range for the return to MkIII* production (B64240 to B76898). Some authors may want to narrow the published serial number range of when the change over took place.
Unfortunately, the No.1 MkIII* is a bitzer but the No.1 MkIII has a matching bolt, action body, and nose cap. I just recently picked it up at an auction for $400 and I'm looking forward to it being a good shooter.