An inmate has been shot dead by a Corrective Services NSW officer after attempting to escape from Lismore Base Hospital on Friday.

The 43-old-male allegedly assaulted one of the prison officers who was escorting him from the hospital following treatment and attempted to escape about 7.30pm.

The inmate was shot after a warning shot was fired, police allege.

He was unable to be revived by paramedics who provided immediate treatment. The incident is now being investigated by both the NSW Police and Corrective Services NSW and will be subject to a coronial inquest.