Mr Rahman sir, I think you are right on the service rifles. The Imperial Russian Army ordered quite a few I understand.
Also I understand some of the Canadian Mounted Police and some Auxilliary units used .303 Brit (Often saddle ring carbines / muskets apparently)
If anyone is interested in "odder" uses of lever action rifles, check out this series from the YouTube channel C&Rsenal
French Contract Winchester 1894:
Russian Contract 1895:
British Contract 1892*:
(For the Royal Navy, the senior bloody service no less! Always were considered slightly "funny" chaps but that's a stretch! Too many long nights away from home and too many "pink gins" under the awning if you catch my meaning)
C&Rsenal are currently releasing a series on the Mauser 98 going through the variants from the original German Gewehr to Serbian, Siamese etc. So the genesis of the best hunting rifles in the world right there. (Not a word, Remington fan boys, you snivelling push-feed-pansies....)