The New South Wales director of public prosecutions is appealing against the acquittal of a Sydney man accused of raping a woman in an alleyway.

Luke Andrew Lazarus, 25, was in early May acquitted of raping the then 18-year-old woman behind Soho nightclub in 2013.

He had previously spent time in jail for the alleged offence before his conviction was overturned and a judge-alone retrial ordered.

“Yesterday I lodged an appeal to the court of criminal appeal against the acquittal,” DPP Lloyd Babb SC said in a statement on Thursday. “As the matter is before the court, no further comment will be issued.”

The woman had alleged she was assaulted behind the nightclub part-owned by Lazarus’ father, Andrew, after meeting him on the dancefloor where he offered to introduce her to the DJ in the VIP area.

The retrial heard the woman fended off Lazarus’ first attempt to have intercourse with her, but was unable to fend off his second attempt.

Judge Robyn Tupman found the woman’s evidence that she said “stop” was unreliable partly on the basis she was wrong about other parts of the night.

Following the acquittal, the woman took to social media and said she felt mad, heartbroken, let down and confused.

“His criminal conviction is erased. He is free to move on with his life,” she wrote. “The reality is this doesn’t get to be over for me.”