The 28-year-old Bland was found dead in her Waller County jail cell on July 13. Bland's family and others have criticized Trooper Brian Encinia, who stopped Bland for failing to signal a lane change.
Video of the stop shows that the confrontation quickly escalated after Encinia asked Bland to put out her cigarette. Bland eventually was arrested for allegedly assaulting the white trooper.
Lambert also expressed dismay that Encinia remains on administrative leave rather than being fired.
Bland's death came after nearly a year of heightened national scrutiny of police and their dealings with black suspects, especially those who have been killed by officers or die in police custody.
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Lambert called on the Department of Justice to launch its own investigation, saying the case needs a fresh and unbiased look.
Authorities said Bland hanged herself inside her jail cell. Her family has questioned that finding.
Calls to Waller County District Attorney Elton Mathis and other county officials were not immediately returned.