Ricky Nelson was one of the most popular singers of the pre-Beatles rock era, and he was also a TV star, appearing on his family's show The Adventures of Ozzie and Harriet. He didn't start writing songs until later in his career when he was no longer a teen idol but a mature singer with a country-rock sound.
"The Last Time Around" is one of the songs he wrote himself. It's a thank you and a goodbye, inspired by a homeless man in New York City who gave him a psychic reading, telling Nelson that he was an old soul with many previous lives, but this was his last time around.
This song was far from a hit (Nelson's chart renewal came a year later with "Garden Party"), but it meant a lot to him. His son Matthew Nelson said in his Songfacts interview: "It's a magical song and you can feel that he took those words that man said and thought it was Jesus speaking to him or something like that. He wrote this amazing song about it that's actually kind of universal."