Two interesting Lithgows serial number-wise.

[Homer]

I tend to put too much faith in what I read in the books I have by Stratton, Skennerton et al. I'm always happy to be of assistance to others when questions are asked but on more than one occasion what I post from the experts turns out to be wrong.

The best most up to date resource for this sought of data is “The Lee Enfield” by Ian Skennerton.
The Lithgow SAF produced MkIII no star from 1913 to 1918, MkIII* from 1918 to 1922, MkIII no star again from 1922 to 1941 and then MkIII* from 1941 onwards