I've never run across a 19th century reference to using lubricated wads in a cap and ball revolver. The earliest printed reference I've found is a 1928 American Rifleman, though it's obvious that it was an established practice in 1928.
Similarly, I've never seen a reference to putting lubricant over seated projectiles to prevent multiple ignition ("chain fire"). When grease, wax or some kind of substance is put over the projectile, it's almost always referred to as a waterproofing measure to keep dampness from the powder, not for lubrication.
That said, I'm sure that the advantages of lubrication were discovered early on, even if it was just a quick spit into the cylinder after loading the chambers (soliders are a practical lot).
There are also references to wax (presumably tallow or beeswax from candles) placed around the caps to ensure waterproofing.
The late gun writer Elmer Keith suggested the use of a lubricated felt wad between ball and powder in his 1955 book, "Sixguns." This is where I first learned of the practice, and began doing so in the mid 1970s. Though Keith wrote that Civil War veterans he knew around Helena, Montana showed him how to load his original 1851 Navy (when he was 12, about 1910), he never once says that they showed him the trick of using lubricated wads.
Alas, some have claimed that such wads were used in the West, but there is no evidence to support this.
I am uncertain what the expected load was for the Walker, when issued to the Army. So few of these revolvers were made, and the use of paper cartridges came after their adoption. When paper cartridges did arrive, they were for the Dragoons. Of course. Dragoon paper cartridges could be used in the Walker.