The Allegheny County Medical Examiner's office said Greenwood died Sunday just before noon from undisclosed causes at Presbyterian Hospital in Pittsburgh.
"L.C. was one of the most beloved Steelers during the most successful period in team history, and he will be missed by the entire organization," Rooney and team president Art Rooney II said in a statement released by the team. "He will be forever remembered for what he meant to the Steelers both on and off the field."
"He was one of those guys who really brought tradition and toughness to our town," Keisel said. "It's hard to hear."
The Associated Press contributed to this report.