The beaten and burnt body was found face down
Detectives say the young man found in Roe Green Park in Kingsbury was beaten round the head and stripped of his clothes before being set alight.
His identity has still not been established, but he is thought to have been aged between 14 and 25.
The graffiti, which reads "Burn Lol", was found sprayed on a yellow grit bin yards from the body.
Detectives admit that Lol can stand for Laugh Out Loud and is a common mobile phone text message.
But they are also hoping that it could have been the victim's name or a so-called graffiti "tag" which identifies the artist.
A Scotland Yard spokesman said: "What we would like to do is find out when it was put there because if it was there a month ago we can rule it out."
Detective Superintendent Nigel Mawer said forensic analysis had revealed several distinguishing features about the victim's teeth.
"He has a congenital abnormality that may be common to siblings and close family.
"He has two lower molars missing and doesn't have any wisdom teeth."
The victim was set on fire with petrol, but no attempt was made to hide the body.