Lawyers for Peter Liang, the former New York City police officer convicted of manslaughter in the shooting of an unarmed man in a public-housing project stairwell, asked a judge on Tuesday to set aside the verdict after they learned, through a newspaper article, that a juror in the case might have lied during jury selection about his father’s criminal past.

On March 26, The Daily News published an article that quoted an unnamed 62-year-old juror at the trial criticizing the decision of Ken Thompson, the Brooklyn district attorney, to recommend probation, not a prison term, for Mr. Liang, who was found guilty in February in the death of Akai Gurley in November 2014. After calling Mr. Thompson’s recommendation “a slap on the wrist,” the juror was quoted as saying that his own father had served seven years in prison for accidentally shooting a friend — an act not dissimilar to the one in which Mr. Liang was convicted.

Court papers filed by Mr. Liang’s lawyers contend that the same juror, identified as Michael Vargas, told the court during jury selection that none of his close relatives had ever been accused, let alone found guilty, of a crime.

“The record demonstrates that Mr. Vargas lied knowingly and for the purpose of securing a seat on the jury,” the papers say, adding that the “falsehood was not accidental or inconsequential” but rather “was a major lie.”