According to this discography, Al Bowlly, vocalist, recorded THE LONESOME TRAIL AIN'T LONESOME ANY MORE with Sidney Lipton and His Orchestra in London in 1938.

Big Bill Campbell, a Canadian cowboy actor and musician who moved to Britain in the 1930s, also recorded THE LONESOME TRAIL AIN'T LONESOME ANY MORE. It was reissued on the album "Rocky Mountain Rhythm," which is still available.

However, I'm not certain that's the song you're requesting. There is also an unrelated song called HAND ME DOWN MY WALKIN' CANE. This makes me suspect that the song you quote is a pastiche of song titles and cliché phrases from various cowboy songs. (Maybe that's why it doesn't make much sense.) Songs of this genre were once very popular. See this thread for other examples.