Nakhon Chompuchat, who is representing two Burmese men accused of the murder, said the victims' friends "should know many things" about what happened.
The bodies of Hannah Witheridge and David Miller were found on a beach in Koh Tao on 15 September.
Suspects Zaw Lin and Win Zaw Htun, both 21, are awaiting trial for the killings amid criticism of the police case.
The migrant workers from Myanmar - sometimes known as Burma - could face the death penalty if found guilty.
BBC south-east Asia correspondent Jonathan Head said prosecutors were ready to put the men on trial, two months after their arrest.
Under Thai law suspects can be held for a maximum of 91 days before facing formal charges.
Our correspondent said: "Despite the claim by the Thai police that they have built a perfect case against the two Burmese defendants, the prosecutor has rejected the police dossier several times, saying it needed improving."
Officers in the country have been accused of poor collection of evidence, reluctance to investigate influential families on Koh Tao and allegations they tortured the suspects to get confessions.
Mr Chompuchat said he was appealing to any friends of Miss Witheridge, 23, from Hemsby or Mr Miller, 24, from Jersey, who may have information to come forward.
"Their friends should know many things about this to prove the true situation," he said.
But the lawyer claimed witnesses were scared to come forward, adding that he had also requested information from a British police team which travelled to Thailand to observe the investigation, and from the British pathologists who examined the bodies after they were repatriated.
Post-mortem examinations found Mr Miller died from drowning and a blow to the head, while Miss Witheridge died from head wounds.
The two men accused of the killing are also charged with conspiracy to murder, conspiracy to rape and robbery.
Failure to seal off the crime scene after the killings and early claims by the police that no Thai person could have committed such a crime have attracted criticism.
Mr Zaw's mother has said her son is being made a "scapegoat" by police and the case has been fixed.
Friends of two British tourists killed in Thailand earlier this year are being urged to come forward as witnesses.