By the time of the Civil War, the Enfield was already being replaced by the Snider-Enfield: the muzzle-loading rifle was being converted to a breechloader. This was as a sort of general push throughout Europe to develop breechloading rifles in response to the very effective Prussian use of the Dreyse needle-gun in combat. So, the answer for the Enfield is, no, they weren't learning from the Civil War, they'd already gotten beyond that.

I am not sure about the history of the Lorenz, but the Austrians had been hit pretty hard by the Prussian army in 1866, using muzzle-loaders, and they would adopt the Werndl breechloader in 1867.

For what it's worth, the US actually supplied the English with much of the specialized machinery used to make the Enfield. The use of special milling cutters, jigs and fixtures pioneered in the Harper's Ferry Armory was further developed in the Robins and Lawrence factory in Windsor, Vermont. Which is now the home of the American Precision Museum.