The incident is reported to have taken place shortly after 1.30am on Saturday January 26.
The victim – a 19-year-old woman – had entered a passageway off Penny Street in company with a man, who then forced himself on her.
Detectives investigating the incident are keen to speak to anyone who can help with their enquiries.
DS Simon Coates, of Lancaster CID, said: “This was a traumatic incident for the victim and she is being supported by specially-trained officers.”
Anybody with information should contact police on 101, quoting log number 951 of January 26th.
Alternatively Crimestoppers can be contacted anonymously on 0800 555 111 or online at crimestoppers-uk.org.