A L.C. Smith, Maker of Baker Gun, Syracuse, N.Y. gun would date to 1880-1884.
From William Wellington Greener,
The Gun and Its Development, 1907, 8th Edition
http://books.google.com/books?id=3HMCAAAAYAAJIn London the barrel-welding industry was never of great importance
since 1844 no gun-barrel welder has practised in the Metropolis. The last maker was W. Fullard, of Clerkenwell, who enjoyed a high reputation for all kinds of sporting gun barrels. The military barrels were obtained from the Midlands, whence, or from foreign centres, the figured barrels used by London makers are now imported.
Some 1870s Parker Lifters have been found with
Birmingham Provisional Proof
c. 1891-1892 Hunter Arms L.C. Smith damascus and laminated steel guns have also been found with Birmingham Proof
I don't believe anyone can document the origin of the "rough forged tubes" used by L.C. Smith Maker, but they were not from London.
We do know this regarding pattern welded tubes in 1895
Nov. 30, 1895
Sporting LifeHow Shot Guns Are Made and the Process Through Which They Pass Fully Explained
The beginning of the manufacture of a gun is the barrels, and it is generally known that no barrels are made in this country except the rolled steel, which is used on the Winchester gun. All gun barrels are now imported, although an attempt was made a few years ago to produce them in this country, but with only partial success. England, Germany and Belgium supply most of the barrels, the latter country doubtless producing the larger quantity. All gun barrels, whether imported direct from the makers in Belgium, or through an importer in this country to the gun manufacturer, are received in rough tubes, which very much resemble a couple of gas pipes, but being somewhat larger at one end than at the other. These barrels or “tubes” as they are called, are merely tied together in pairs, with small wire and 40 to 50 pairs are packed in a box.