With the common name of all common names, that is a tough order to fill, i.e. finding what happened to him (and I am sure your father realizes the unlikelihood of his still being alive at around 94ish).

Still more detail is needed. I made a couple quick checks of the census in 1920 and 1930 but do not find a lulu smith with a son John A. Obviously it would help to identify some of his family like siblings or nephews/nieces to ask about him.

My suggestion at this point is for you to try to locate the divorce record and the associated marriage record. The marriage record in particular may have parental information.

Also if you have not already done so, you could try working your grandmother's family for information, especially the women. Female relatives by marriage have always provided me with more information on their husbands' families than the husbands themselves.

The bottom line is that you need to find much more information so that you can know if you do come across a record of your grandfather that it is indeed his.

Locating your grandparents' marriage record is especially important as it may lead to his family. At that time in Kentucky marriages were recorded on the county level only. So you need to know the county.