The victim, a 19-year-old man, was punched in the face outside the McDonalds in Cheapside at around 3.30am on Saturday, November 27.
Police said the man was left with a broken jaw which required surgery following the attack.
Today (December 6), police released CCTV images of a man they wanted to identify as part of their enquiries.
DC Mark Nelson, of Lancaster CID, said: "The victim was punched to the face in what was an unprovoked attack.
"He has since had to undergo surgery on a broken jaw.
"We would like to identify the man in the image as part of our investigation and are asking anybody who knows who he is to get in touch with us straight away."
Anybody with information can contact police by calling 101, quoting log number 480 of November 28.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555 111 or online at crimestoppers-uk.org.
It is thanks to our loyal readers that we can continue to provide the trusted news, analysis and insight that matters to you.
For unlimited access to our unrivalled local reporting, you can take out a subscription HERE and help support the work of our dedicated team of reporters.