A classic lever-action repeating rifle from the 1890s, this weapon was one of the late models of the original series of Winchester repeating rifles from the second half of the 19th century.
It is present at Westworld (film series continuity), visibly stored on weapon racks at a local sheriff's office. Only one character is seen using the Model 1892, The Gunslinger.
Early Lever-Action Rifles Volcanic, Henry, Winchester
Video on the historical development of lever-action rifles (ForgottenWeapons.com)
Winchester Lever Action Development Model 1892
Video on the historical development of the Winchester Model 1892 (ForgottenWeapons.com)