New York state is expected to ask a judge today to make public a grand jury’s investigation of the Tawana Brawley case that reportedly concludes the black teen-ager lied when she said she was kidnaped and raped by six whites. Atty. Gen. Robert Abrams likely will go before state Supreme Court Justice Angelo J. Ingrassia to ask that he release the grand jury report, said Gary Fryer, a spokesman for Gov. Mario M. Cuomo. Lanie Accles, spokeswoman for Abrams, said she had no comment on any anticipated actions by the grand jury. The New York Times reported last month that the grand jury concluded overwhelming evidence indicates the 16-year-old former Wappingers Falls girl made up the story, perhaps to avoid punishment for late nights out.