The City Directory for Ironton, OH, 1935, lists John J. but also lists Sarah, widow of John J. At the same address were Arthur and Harold. Clyde J. had wf. Nellie (Ancestry.com).
Have you checked city directories for Lexington, KY, for the name of Arthur's wife?
Have you checked on all of his siblings and their obituaries? Do you have the married names of his sisters so that you can find when and where they died on the Social Security Death Index?