Bush and his wife were in Charlotte to sign copies of their respective memoirs, Decision Points and Spoken From the Heart.
Franklin Graham said the former President and his father have been friends for 30 years.
During the lunch meeting, the two reminisced about fond times together, including summer vacations in Kennebunkport, and Graham asked how Mr. and Mrs. Bush senior were doing, he said.
In Decision Points, President Bush recalls a conversation with Billy Graham that helped turn his life around.
"He made it clear that the path to salvation is through the grace of God," Bush says of the world-famous evangelist in the book's first chapter. "And the way to find that grace is to embrace Christ as the risen Lord-the Son of a God so powerful and loving that He gave His only Son to conquer death and defeat sin."
"My father is very grateful that he had an opportunity to speak to the president at a point when the president was willing to listen. He does remember the moment," said Franklin Graham, who has continued his father's mission by serving as CEO and president at the Billy Graham Evangelistic Association.
The younger Graham, CEO and president of Samaritan's Purse, also gave Bush an update on his recent trip to Haiti as part of the relief ministry's effort to address the cholera epidemic in the country.
"Haiti has got great problems and it's not going to be fixed easily. It's like an elephant – how do you eat an elephant? One bite at a time," said Graham.
Franklin Graham said he extended the invitation to the former first couple last week and to his surprise they said they had an opening on Monday.
About a thousand people stood in line for hours to get a chance to speak to the former first couple.
Bush signed a lot of books ahead of time because he wanted to shake the hands of the people in line and thank them for coming, according to Graham.
"I appreciate that about the president," he said.
Bush has sold more than 1.75 million copies of his book since its release early November. Laura Bush's book, which was released in Spring, also spent many weeks on the USA Today bestsellers list.