"We had just moved into our new house, and I was taking out some garbage while she was backing out of her driveway," Abernathy said during a recent phone interview.
"She stopped to introduce herself and welcome us to the neighborhood," he added. "I told her that I was a musician also, and we've been friends ever since."
Abernathy will perform Saturday on the Bell Auditorium stage where Lee, a former Augustan, was discovered in 1956 by Grand Ole Opry star Red Foley.
Abernathy and his longtime companion, Jane Hooper, have lived across the street from Lee and her husband, Ronnie Shacklett, for about 10 years. They have another Augusta connection: Hooper's daughter, Dudley, is married to Augusta neurosurgeon Marc Guitton.
"Brenda and Ronnie are just great neighbors," Abernathy said. "We love them to death. Ronnie was just over here mowing our grass, and, whenever either one of us are sick, Brenda is over here with her chicken noodle soup. We've been over to each other's houses lots of times."
Abernathy, who has performed in 94 countries, was surprised when he learned that Lee and B.B. King often had performed on the same bill.
"Brenda even gave me a poster that had her and B.B. appearing on the same show," he added. "She's just a great person who always makes you feel good just to be around."
Abernathy said one of the great things about living in Nashville is becoming friends with so many great musicians of so many different musical backgrounds.
"I do cross paths with quite a few country stars, and I have a lot of friends who play in their bands," he said. "It's an interesting mix of musicians in Nashville, including all of the inspirational artists. I've also lately been meeting a lot of musicians from overseas coming to Nashville to record."
Abernathy's background includes performing and touring with Nancy Wilson, Gladys Knight, Diahann Carroll, Sammy Davis Jr., Albert King, The Manhattans and The Chi-Lites.
Playing on the road with Bobby "Blue" Bland for 13 years led to his long gig with B.B. King.
"Bobby and B.B. for many years were a package show together. Bobby developed problems with his heart, and I asked B.B. to take me on to pay the bills. I've now been with him 17 years."
In addition to recording on King's albums, Abernathy has his own CD, Only When I Think Of You , and expects to have a second, It Ain't Easy Being Me , released this month.
"Being a horn player, it's a smooth jazz album," he said of the new CD. "I've managed to capture a blues feeling with it, but it still has an international flavor."
Living across from great neighbors, having a loving companion such as Hooper and traveling with a great musician makes life good, he said.
"It's all about being in the right place at the right time. I've been very blessed and fortunate in my life."