I am not fully up on their history but L C Smith began in partnership with W H Baker as I recall. Early guns were Baker's designs. I know that some of these early guns were marked L C Smith Maker of the Baker gun or something on that order. Some of these were drilliongs or three barrel guns having two shot barrels & a rifle barrel. The L C Smith was one & the same as the one who would give the name to the L C Smith gun which was in fact designed by Alexander Brown. Smith was not a gun designer. He would eventually sell out to the Hunter Brothers who made most of the L C Smith guns & He & Brown went into the typewriter business.
Someone else will probably be along & fill in missing details as well as correcting any of my errors. As far as I am aware of though there was only one L C Smith, Lyman Cornelius Smith to be precise.