Bolanle Raheem was reportedly struck by Drambi Vandi as she and several family members were on their way home from a church service.
The slaying of the lawyer, who was carrying twins, has shocked a lot of Nigerians.
Justice has been requested by the Nigeria Bar Association and human rights organizations.
The association’s Lagos branch announced that it would file a lawsuit against the police and seek $10 million (£8 million) in damages for Ms. Raheem’s family.
According to her mother, who was cited by local media, she sold oranges as a hawker to pay for her daughter’s legal education.
“She was removed from my presence. She was expecting twins “The mother of Ms. Raheem stated that she had also left behind a daughter who was five years old.
Police chief Usman Alkali Baba urged the public to “remain calm” and vowed to continue working to guarantee the lawyer receives justice.
Police brutality in Nigeria has received more attention in recent years.
The controversial Special Anti-Robbery Squad (Sars), which was the target of widespread protests under the hashtag #EndSars, was dismantled in 2020 as a result.