Stewart Rexter, 38, was found in Victoria Place in Airdrie at 17:30 on Thursday.
Detectives believe he was attacked by a man described as being between 25-35 years old, 5ft 8in, of slim build with short dark hair and dark clothing.
They are also keen to trace the occupants of a dark Transit-type van seen nearby.
Mr Rexter, who was from Coatbridge, was taken to Monklands Hospital and then later transferred to the Queen Elizabeth University Hospital in Glasgow where he died on Saturday.
Det Ch Insp Paul Livingstone of Police Scotland's major investigation team said: "Officers have been carrying out extensive inquiries into this incident including carrying out house-to-house inquiries and studying CCTV footage gathered from the local area.
"We believe that Stewart was attacked by a man around 17:10 hours in Victoria Place between Craig Street and Devonview Street.
"Inquiries are ongoing to trace the man who is described as white, 25 -35 years old, approximately 5ft 8 inches in height and of slim build with short dark-coloured hair and wearing dark-coloured clothing.
"In particular, we are keen to trace the occupants of a dark-coloured Transit-type van that was parked on Victoria Place opposite the entrance to Airdrie train station.
"I believe that the occupants of the van may have vital information that would assist this inquiry and I would urge them to come forward."
A murder investigation is under way after a man found injured in a street in North Lanarkshire died in hospital.