Lloyd - Siemens-Martin process steel was likely made all over the world. And it is clear that the composition and strength thereof changed over time.
I know little about that new fangled fluid steel stuff, but following the introduction of Krupp Fluss Stahl and Krupp Nickel Steel, both about 1890, gun barrel steels changed (for the better) rapidly.
Winchester Nickel Steel was introduced for the Model 1894 rifle about 1896, Marlin “Special Smokeless Steel” was introduced for the Model 1893 rifle in 1897, and Remington Ordnance Steel was introduced in 1897 for the 1894 Hammerless Double; all with tensile strength 100,000 - 110,000.
Hunter Arms introduced Crown steel with their Pigeon Gun in 1893.