Lyon & Healy was a huge Chicago music store. They did have a workshop where some banjos (and other string instruments were made) but the L&H name also was put on banjos (etc) that were made by several different makers. The quality was all over the place. Great, good, fair, bad, horrible. I've played about half dozen that I can recall. Most were ok, not-too-bad, nothing exceptional. But I was exposed to a random sampling.
L&H are still building harps in Chicago. I think their banjos were made by jobbers like Tonk Bro., Regal, etc. There were a number of jobbers in the Chicago area throughout the 1880-1920 period. Lots of mandolin makers too. Schall may have made their higher quality banjos.
I have a L&H "Mystic" model, just a basic no frills banjo. Serviceable but nothing special.
I have a late 1880's flush fret L&H called "The London" which I read somewhere was most likely produced for export. Which I guess is how it came to be in the UK!
Rather like Trapdoor's its fine but nothing to write home about.
I own a L&H Mystic. I got a great deal on it, but it was disappointing. Later I tuned it up one step and it really shone! By the way, I worked at the L&H harp factory around 1972 as a gilder.