From Billboard, August 14, 1965, page 28:

Also receiving strong plugging is "Laura Lee" a title from the Columbia film "Major Dundee." T. M. Music arranged with both RCA and Capitol to have singles on the title released by Eddy Arnold and Wayne Newton.

"Major Dundee" (directed by Sam Peckinpah, 1965) was a western set during the Civil War, which probably gave rise to the idea that the song dated from that era.

IMDb.com says that the song LAURA LEE, from the film "Major Dundee" was written by Liam Sullivan and Forrest Wood.