One thing to keep in mind, When Mr Speed/Lee and Metford/Enfield put their products together to bring about the rifles we commonly group together as Lee Enfields, they were considered to be BEST RIFLES for hunters and most commoners just couldn't afford them.
The components were available to entrepreneurs just about anywhere in the world, but mostly in the UK.
The competition was for the most part commercial Mausers and in some cases, Double rifles.
There were a lot of single shot, bolt rifles, break action and falling block variants available and in most of th world that is what was used to hunt with.
Early Mauser/Lee magazine rifles were cutting edge tech when they first appeared on the markets.
Didn't take very long for both of them to garner large followings.
As for lever actions, they weren't unpopulare but they were also expensive and limited in power in some cases. That isn't saying there weren't some very powerful cartridge chamberings offered in them at the time.
If the OP is only talking about North America, lever action firearms seemed to play more of a role than they did in Europe. But to consider their impact on the rest of the world, not so much. The Russians liked the M95s enough to adopt them for their military. I believe France adopted US made lever actions for limited military use as well.
For the average commoner, IMHO it wasn't until after the early Lee Metfords had seen a few years of military service' proven themselves and later sold out of service onto the surplus markets around the world, that they became available at a price that was affordable.
