Nice Remington!
Looks like it could be a Model 30-S Express.
Does it say Model 30 / Express on the left side of the front ring?
Or does it say Model 30-S / Express..
They had Model variations for just about everything including factory mounted optics and specialty aperture rear sights.
Model 30S (S-Special) was a variation of the Express. It was their Deluxe version of the rifle. In the early 30's it was changed to Model 30SL.
Lot's of options. They even had different Model designations for the rifles ordered w/factory installed optics and specialty aperture sights beyond the standard Lyman.
I'd say a 7x57cal is a real find,,can't recall ever seeing one in the flesh myself. Usually 30-06, a 25Rem made over to 257Roberts or a cobbled up rechambered HV modern magnum conversion of some sort.
That Lyman Alaskan is a beauty too,,not an easy scope to find anymore in nice condition.
Congrats!