Lyman was initially asked to make the scopes for the 1903A4, but they detailed that they could not produce the number required by the dates needed and therefore would decline. That is how Weaver got the contract.
The Lyman Aslaskan was going to be called the M73 scope for the A4. Actually the very first ones were marked M-73 by Lyman, even for the M1C. But lyman still had not shipped the first shipment in Nov 1944. Ordnance changed their mind on the M-73 name and actually directed the scopes to be marked M81 instead. Before they left the factory the few that were marked M-73 had the 73 marked out and the M81 markings applied on the tube. I have one of those scopes.
Ordnance did not receive the first M73/M81 scopes till about December 1944. They detail they put them on the first 350 M1C's and shipped them out by Jan 1945.
The whole reason they the M81 (crosshair) existed is Lyman could not get the tapered posts for the M82 scope, that is why the first ones shipped with crosshairs and why the M81 existed. Ordnance from the beginning did not want the crosshairs, and only wanted post reticules. But they took them because they were in a hurry to get the first Garand snipers to the field.
The M-73 marking, with the 73 marked out.
Here is the M81 marking added. The scope still retains all the original Lyman commercial markings as well.