Searching the SSN death index for Kenner in TN and KY I get only one with an I and no Lucilles so one of his wives may still be alive:
I KENNER23 Dec 1922 Sep 1987 Clinton, Anderson, TN 37716415-16-2150 Issued in Tennessee
But obituary times finds KENNER, Lucille ( ); 73; Medford OR; Mail Tribune; 2001-2-13; billeter
Searching public records for Lucille Kenner finds only one in Baltimore MD.She could be using L Kenner then it gets harder since there are a lot of L Kenners tho there are none in Clinton TN.
However, Anderson Co is near Knoxville and there is a Randy Kenner, staff writer on the Knoxville paper.Perhaps if you email him he will look up the obit for you.If there is one it might help you find some kinfolk.