Haeyoon Miller's mother and father filed separate claims within the last two weeks.
A 60-foot tree fell on September 15 near the intersection of Irvine Avenue and 17th Street, landing on a Hyundai that was stopped at a red light.
The driver, 29-year-old Haeyoon Miller died of injuries sustained when the tree crushed her car.
The lawsuits allege that the city was negligent in its care of the 10-ton, 70-foot-tall tree, which fell from Irvine Avenue's median in September and crushed Miller's small sedan.
The city was well aware of their danger, Suk alleges in her claim, because eucalyptus trees previously fell nearby.
Suk alleges that the city tried to conceal evidence when it removed and destroyed about 100 eucalyptus trees from that stretch of Irvine Avenue, soon after the accident.
City officials have declined to release the results of an investigation into the tree's collapse, citing pending litigation.
Chung also alleges that emergency responders failed to stabilize the tree after it fell, a mistake that "caused or contributed" to Miller's death.
After the accident, witnesses said that firefighters began to lift the trunk when it dropped again on the car.