OK so I found his obituary, starts like this:
''Larry E. Rood, 87, died Monday, July 7, 2003 at Community Hospital South in Indianapolis. He was a resident of Indianapolis, Indiana. Mr. Rood was born August 20, 1915 in Omaha, NE. His parents were Edward and Ruth (Shirley) Rood. He married Katy L. (Addison) Rood on June 13, 1937 in Indianapolis.'' (I omitted the details of his surviving family).
So *naturally* one would expect 'Larry' to be short for 'Lawrence'... oh no. It's Laural. *le sigh*, LOL. Here he is with his wife in the 1940 Census.
And that is apparently all I can find. I just can NOT seem to find him/his parents in previous Censuses, or his parents' marriage record.
Maybe someone else might have more luck?