Evaldas Simanaitis, 68, is thought to have been injured after confronting a thief or thieves trying to steal his car, and died in hospital 10 days later.
One man has been charged in connection with the incident, but police on Wednesday released an image of a second man they are keen to speak to.
They say he "should not be approached by the public", and urge anyone who sees him to call 999.
Police were called around 4.45am on October 16, to reports of two men breaking into cars in Boundary Lane, Newham.
They arrested a 25-year-old man at the scene, who was found to have on him a car key registered to a property less than four miles away, in Matcham Road, Leytonstone.
Officers went to the property, where they found Mr Simanaitis seriously injured.
He was rushed to hospital by ambulance in a critical condition. Despite the efforts of medical staff, he died 10 days later, in the early hours of October 26.
CCTV revealed Mr Simanaitis had been injured outside his home around 4am on the day he was found.
A post-mortem examination found his cause of death to be a head injury.
A 25-year-old man has been charged in connection with the investigation.
Scotland Yard now urgently wants to speak with a man - who officers believe to be 24-year-old Tomas Asmenkas - who is thought to have been in the area at the time of the incident.
Officers are keen to hear from anyone who has seen him, and are also appealing for Ms Asmenkas to contact police directly.
Detective Inspector Aytac Necati, from the Met's Specialist Crime Command, said: “I would urge you to look closely at the image we have released today. We need to speak with this man as a matter of urgency about the events that night.
“Mr Simanaitis’s family are facing Christmas without him. Please put yourselves in their place. Someone knows where this man is; please do the right thing and contact us.
“If anyone saw or heard anything on Boundary Lane or Matcham Road in the early hours of October 16, but has not yet spoken with police, I ask them to please come forward.”
If you have information relating to Tomas Asmenkas' whereabouts please call 101 quoting reference 847/16Oct.
To remain 100% anonymous contact Crimestoppers on 0800 555 111.