Lee asked for the probe of the Mario Woods shooting in a letter to U.S. Attorney General Loretta Lynch that was made public on Monday.
The letter said that Lee is "inviting transparency and accountability" in the department.
"We seek answers, not just to the facts of Mr. Woods's case," Lee said, "but also answers about how as a Police Department and a City we can build deeper, stronger trust between law enforcement and the communities they're sworn to protect."
Many, including Woods' family, had urged the mayor to ask for the probe, and Lee was joined in the request by city supervisors London Breed and Malia Cohen.
An after-hours message left with a Department of Justice spokeswoman asking for a response to the letter was not immediately returned.
The furor over the Woods shooting dominated the end of Lee's first term and the start of his second, which began earlier this month. His inaugural speech was interrupted by angry protesters, as were remarks he made on Martin Luther King Jr. Day.
Police were responding to a stabbing report in the city's Bayview neighborhood on Dec. 2 when they encountered and surrounded the 26-year-old Woods. Five officers shot and killed him after he appeared to raise an 8-inch knife and approach an officer, according to police.
A KQED analysis of an Instagram video showing the fatal shooting appears to contradict claims by Police Chief Greg Suhr that officers opened fire only after Woods made a threatening movement.
Woods' family has disputed SFPD's account of the killing and filed a lawsuit against the department. Their attorney has said he was not aggressively fighting the officers, who should have backed away.