Lindsey Graham's Military History

I don't have anything definitive, but for those who were curious about this:

Webb: “Because they love their country. (cross-talk) They do not do
it for political reasons. Believe me, my family's been doing this
since the Revolutionary War.”

Graham: “Yea? Well so has my family.”

A scan of news databases shows that Graham has never mentioned this history of service before, the Sons of the American Revolution (a voluntary organization) doesn't have him listed as a member (though there were Grahams that served), and his Senate office has not responded to requests for further biographical data.