Lever actions are uniquely American for a few reasons.

It was individual "civilian" Americans that explored/conquered much of the West.

Playing Cowboy and Indians... It was a big advantage to have a repeater.

Even though our military stuck to the single shot for much of this time, the "civilians" traveling in smaller numbers, quickly realized that the "gun you loaded on Sunday and shot all week" was essential to survival on the Frontier.

By the time "repeaters" were mainstream rifles, Europe had been pretty much "civilized", and common folk were under feudal rule and did not have the same freedoms, rights,or land expansion possibilities of America.

The same applied to the handgun.