The collision happened in the early hours of Saturday October 2 at around 1.45am on the B1363 Wigginton Road between the railway line and the old Bumper Castle pub.
The lorry was travelling out of the city towards the ring road.
Officers are are appealing to anyone who witnessed the incident or saw a man in dark clothing walking along Wigginton Road between the Crichton Avenue junction and Bumper Castle in the early hours of Saturday morning.
Dashcam footage from those in the area at the time is also being sought.
Anyone who can assist the investigation is asked to contact North Yorkshire Police on 101, select option 2 and ask for Sergeant Julian Pearson or email [email protected]
The man, who is aged in his 40s, remains in hospital with serious injuries.
The road re-opened at 8am on Saturday.