Welcome and neat gun.

Could you please look in your 1905 D.M. Lefever & Sons The New Lefever catalog and post the steel listed for the other grades?

I've found:
Excelsior with Washington (not American Flag) Damascus
https://www.gunsinternational.com/guns-f...un_id=100627037

9F with Imperial
http://www.dogsanddoubles.com/2019/03/auction-alert-insanely-rare-16g-d-m-lefever-16g-sxs-9f-grade/

There was an Imperial Steel Co., Cleveland in 1910, but it was not listed in 1903.
https://books.google.com/books?id=rj80AQAAMAAJ&pg=PA73&lpg

9E Krupp
8E Nitro & Krupp
http://www.dogsanddoubles.com/tag/d-m-lefever/
7D Krupp

Bottom line:
1. The U.S. makers could creatively label their barrel steels with whatever name they wished. D.M. Lefever & Sons may have chosen Imperial because of the proximity to Imperial Steel, or maybe simply because it sounds Royal wink
2. The fluid steel "rough forged tubes" were (almost) all sourced in Belgium
3. We have actual composition data for very few, but thanks to Dave Suponski know that at least there was a minor difference in named Parker barrels
https://docs.google.com/document/d/1dnRLZgcuHfx7uFOHvHCUGnGFiLiset-DTTEK8OtPYVA/edit
4. We don't even know the composition of Krupp Fluss Stahl (Homogeneous Fluid Steel) introduced about 1890 and used on pre-WWI barrels, but published data suggests it was similar to AISI 1045 with an industrial standard ultimate tensile strength of 85,000 psi.
5. There is no reason to think that a quality U.S. maker used anything but quality (for that period) barrel steel.

BTW: Lefever Arms Co. was the first U.S. maker to supply Whitworth steel for their Optimus in 1887.
The first Lefever with Krupp steel barrels was in 1894.
c. 1900 C & D grades may have Ordnance Steel barrels
Outing, Oct. 1901
https://books.google.com/books?id=5RALAAAAIAAJ&pg=PA128-IA12&lpg

In 1912 Lefever Arms listed the DS with Dura-Nitro Steel, the H with Carman Fluid Steel, G with Royal Nitro Steel, and the F with Premier Nitro Steel.
I haven't found a "Carman" steel works, and about everyone had some kind of "Nitro" steel