Twenty-year-old Pedro Espinoza, an illegal immigrant and alleged gang member, is charged with the murder.
Shaw's parents and brother claim the county and sheriff's department violated immigration laws and their civil rights by releasing Espinoza from jail just one day before the killing.
According to the lawsuit, deputies were negligent in releasing Espinoza, who was known as "a dangerous felon and an immigration violator."
A sheriff's department spokesman declined to comment on the lawsuit.
The Shaw family is seeking unspecified damages.
They were unsuccessful in a recent drive to put what was called "Jamiel's Law" on the city's May ballot.
It would have given Los Angeles police officers the right to arrest undocumented gang members before any crime was committed.
Currently, the LAPD operates under Special Order 40, which is in place so undocumented residents can report crimes without the fear of being deported.
It prohibits officers from contacting suspects solely to ask about their immigration status.
Espinoza is due back in court on June 30.
AP & CNS contributed to this report.