The guitarist had been dealing with health issues over the past couple of decades.
Rhodes passed away at his home in Nashville, Tennessee, the morning of March 4.
Lindley's guitar and fiddle skills made him a go-to collaborator for Jackson Browne, Dolly Parton, Bob Dylan and others.
The musician joined the band in 1989 and played on five of their albums.
"Anthony was a complex character," his brother-in-law Joe Henry wrote on social media.
The private equity pioneer was found dead in his Manhattan office on Thursday (Feb. 23).
He also wrote the lyrics for the film's "Danger Zone," performed by Kenny Loggins.
Smith was one of the last survivors of a scene of music artists who helped make New Orleans a fundamental influence on rock ‘n’ roll.
The Emmy winner and Oscar nominee befriended Stanley Kubrick on a Bronx baseball field, then scored his first four features.
His death comes just weeks before De La Soul's classic catalog is set to finally arrive on streaming and digital platforms on March 3.
