This definitely appears to be John Henry Lail b. Jun 20, 1940 at Garvin OK, d. Dec 29, 2003. at Brooksville, Hernando, FL. He was the son of Homer Jackson Lail b. 1907, d. ___. and is part of the Henry Lail (1754) branch which is found in parts of MO, AR, OK, and TX.
Sorry to say I don't have anything on any children of your father. However I can see 2 good possibilities;
1) Your Dad had a full sister named Louise who may well be traceable.
2) Homer (your GF) and one of Homers brothers married sisters and I have decent info on that family. Being double first cousins should mean a better chance of someone knowing something helpful.