Lybarger rights protect peace officers from being compelled to incriminate themselves during investigatory interviews conducted by their employers. It refers to the Lybarger v. City of Los Angeles (1985) brought before the California Supreme Court. The case involved an LAPD officer who was brought before Internal Affairs due to misconduct and malfeasance, an investigation which he refused to cooperate. The case was overturned because he was not properly informed of his rights. Lybarger warning is similar to Garrity Rights for other public sector employees.
When Nolan is discussing divorce with Gennifer, he says his mother covered for his dad by saying he was a spy. In Castle (2009), Nathan Fillion's character Richard Castle's dad was a spy for the CIA.