Chuck
These are great leads--just what I'm looking for. Thanks.

Thanks Frank,

You caught some important things on the table that I needed to correct. I've updated it, and like it a little more. 

I'm now leaning a little toward re-lining for a 38-55 marked "for black powder only." However, I also notice in the table that the performance of the 44-40 and 38-40 is quite close to that of the black powder version of the 38-55, and I wouldn't have to do my own hand loading or clean it between every shot. So that 44-40 is looking quite tempting. I'll need to think on this for a while and talk to the smith.

As someone said 2000 years ago, I'm almost persuaded.

The saga of my grandfather's 1885 LW, built in late 1888 continues:

It was re-barreled to a 45-70 Winchester barrel, just before my grandfather bought it, sometime in the late 1920's. So, it MAY have a higher quality steel in the barrel than the original barrel. I've looked and cannot find any mark indicating the quality or type of steel for the barrel, but I don't know what to look for. Is there any mark that was commonly used that could trace this barrel to indicate the quality of steel? If it's a good quality steel, I assume that I could consider getting it relined to a smaller caliber.

I realize that the pressure against the block is still a major consideration, but possibly the barrel strength is now less of a consideration, if there is some way to verify the type of steel in the barrel.

It looks like it's marked VP in a circle just behind the notch for the sight.

Chuckster wrote on Sep 13^th, 2016 at 4:06pm:

I ran across a Stevens 044 1/2 that someone had bored out the original 25-25 barrel to try to convert the rifle to .410, and fortunately had stopped there.
Was able to buy it at a really nice low price, and turn it back into a nice CF rifle once again.

If I find another barrel on-line, is there any way for me to know if the barrel threads will match the receiver? As I understand it, my receiver is probably a small threaded variety but Winchester came out with larger threaded barrels in later years. Does that thread change occur in only selected calibers or in all calibers?

Not later years- both small and large coexisted. Bigger size to accommodate larger rounds. Like with the lower walls, the small shank is suited to small rounds. Never saw an original small shank in either frame that was for a big case.
If the 'found' barrel is a take off from a small shank low wall the chances of it fitting are fair. Most interchange pretty well, not all. Don't forget that it will need an extractor to match.
And, don't go thinking you'll get a .38-55 or such in a small shank takeoff barrel. Ain't likely at all.