I saw a question similar to this one in the r/NoStupidQuestions subreddit and one of the responses said that Europeans basically skipped over the lever action repeaters and went straight from single shot rifles to bolt action rifles and that the lever action guns were pretty much a purely American gun. Why was that?
More can be written on this, but you might be interested in this previous discussion: "Why did militaries favor bolt action rifles rather than lever-action rifles throughout history?" . Counting the replies there and the two linked discussions, there were replies by /u/PartyMoses , /u/Mrprocrastinaut , DanTheTerrible , and /u/laduke_loves_cope .
This is not to discourage discussion. More questions, data, and debate are welcome.
If you want to count the Turks as a European power, they did in fact buy a good number of Winchester Model 66 rifles and use them against the Russians in the Russo-Turkish War, notably to great effect in the Siege of Pleven, in Bulgaria. The Russians were largely equipped with breech-loading single shot Krnka rifles. The Turks had also bought breech-loading artillery.
Just because the Winchester did not get adopted by other European powers did not mean it did not have an effect. The Swiss quickly incorporated the tubular magazine and cartridge-lifter- feed design of the Winchester into the design of their bolt action Vetterli rifles. Austrian Alfred von Kropatschek took the tubular magazine idea, discarded the Winchester cartridge lifter for one of his own ideas, and those improvements were incorporated into the Mauser rifle in 1884: which was bought by the Turks.