Ken: I agree with PeteM that the vast majority of lopins were "stacked" at the rolling mill:
"There is a general myth which goes something to the effect that each barrel maker made the pattern. That is simply not the case. The rolling mill would schedule runs of the patterns it had orders for. The barrel smith would pay the mill for the ribbons they needed. The barrel smith would then forge them into complete barrels..."

HOWEVER, per Monthly Consular and Trade Reports, “Report by Consul Robertson on the Manufacture of Fire-Arms in the District of Verviers and Liege”, 1885
https://books.google.com/books?id=7EhJAAAAMAAJ&pg=PA136&lpg
The lopin was stacked by the barrel maker, then sent to the rolling mill.

It is my opinion that proprietary or complex (think words in the pattern) lopins likely originated with the barrel maker.
"Runs" of generic damas' crolle rods originated at the mill, and as the process became more refined and mechanized, so did the ribbands. The 1891 Birmingham Proof House Trial Report listed a bunch of "machine forged" pattern welded barrels. Someone's eyes and arms still had to helical weld the ribband into a barrel however.

The barrels “in order of merit of endurance” (strength) were judged by the Guardians of the Birmingham Proof House to be:
* Tied for first place in the second phase destructive testing
1. English machine-forged 3 rod Laminated steel
2. English fluid compressed steel, Whitworth process
3. English machine-forged 2 rod Best Damascus
4. English steel Siemens - Martin process *
5. English hand forged 4 rod Best Damascus
6. English machine-forged 2 rod variegated Damascus *
7. English machine-forged 3 rod Best Damascus
8. English carburised steel, Darby’s method (invented in 1890 to add carbon to steel)
9. English machine-forged 2 rod Laminated steel
10. English “Superior Barrel Steel” (process and source not documented) *
11. English machine-forged chequered 3 rod Damascus (no clue as to what pattern this might be - have never seen a British "Bernard" pattern) *
12. Foreign steel, Siemens - Martin process *