Lyman Alaskan’s are great vintage scopes. It’s essentially the same as the US M81 sniper scope, except it lacks the sun shield, rubber eye piece and US markings. The US M82 was similar, but had a post instead of crosshairs. It seems that post reticles are more desirable on commercial versions. The US had a hard time getting enough scopes during the war, so it’s reported that some commercial Alaskan’s were used on Garand and 03-A4 Snipers.
Alaskan’s are approved for CMP sniper matches, which adds to their desirability. You’ll also see them on period Griffin & Howe Sporter’s in G&H detachable mounts and on Winchester Model 70’s/Savage 99’s in Stith no-drill mounts. These mounts can bring as much or more than the scopes.
Your Alaskan appears to be in Weaver tip-off rings for a .22 and they’re only worth around $20. Your scope looks pretty clean and it would probably bring somewhere between $200 - $300 at auction.
FYI, those have 7/8” steel tubes. They weren’t nitrogen purged and it was necessary to remove the ocular bell to install the early Redfield rings. These originally had flat rubber washers that help seal between the turret housings and the caps and they tend to deteriorate and tear. You can find suitable replacement rubber O-rings in the bulk trays at ACE/ACO Hardware for about $0.50 each.