Bonus info and pictures!
It turns out that the inscription on the lid of the case reads:
R. S. Hunter - Blair
Gordon Highlanders

After a brief google search it turns out that Captain R. S. Hunter Blair was in the Gordon Highlanders(a Scott Regiment in the British Army until 1994) starting in 1881! It would be interesting to find out any additional history on the good captain and how this rifle ended up in US.
https://www.dropbox.com/s/n4hr2742qdi7qul/IMG_4893.heic?dl=0
https://www.dropbox.com/s/nclwjiiwh34r7s9/IMG_4895.heic?dl=0
https://www.dropbox.com/s/fl0ptfumxqsc16d/IMG_4897.PNG?dl=0
https://www.dropbox.com/s/wiyk60pbmcgy0cr/IMG_4893%20%281%29.heic?dl=0