The fifth man has not yet applied for legal aid for a judicial review of his summons to give evidence to the inquiry.
A Legal Aid Board spokeswoman said: "So far we have received four formal applications and all four have been refused.
"One of those four is appealing against the decision."
The five men - David Norris, 21, Neil Acourt, 22, his brother Jamie, 21, Luke Knight, 20, and Gary Dobson, 22 - have all at various times been charged with Stephen's murder.
Neil Acourt, Dobson and Knight were acquitted at the Old Bailey in 1996. The charges against Jamie Acourt and Norris never came to court.
The five have been summoned to appear on 8 June before the public inquiry investigating the murder and the police response to it, which is currently hearing evidence in south London.
Last month lawyers for the five announced they would ask a judge to rule the summonses unlawful.
They said they would seek a ruling that either the terms of reference of the inquiry are too broad and therefore unlawful, or that the questions due to be put to the men go beyond those terms of reference.
The men are understood to object to proposed questions about their activities before the 1993 murder. The inquiry was set up to look at "matters arising" from Stephen's death.
Stephen, 18, was stabbed to death at a south London bus stop in what an inquest jury decided was a "completely unprovoked racist attack by five white youths".
No one has ever been convicted of his killing.
Decisions to grant legal aid are based on a means test and a merits test - whether there are "reasonable prospects of success and whether it is reasonable in all circumstances to grant legal aid," the Legal Aid Board spokeswoman said.
Without legal aid, the men will have to fund the applications for judicial review themselves.
No application for judicial review in this case has so far been received at the Royal Courts of Justice.
The summons ordering the five men to attend the Lawrence inquiry has been put back a week to 15 June.
Michael Holmes, solicitor for one of the five, Gary Dobson, said his legal aid application had been turned down on the grounds that it was "speculative".
"You could say that about any litigation," said Mr Holmes.
Dobson's appeal against the refusal will be heard by the Legal Aid Board's Area Board next Monday.
During yesterday's hearing, the senior detective supervising the Stephen Lawrence murder investigation angrily denied allegations that he was corrupt.
Detective Chief Superintendent William Ilsley, who is now retired, responded heatedly to questions over the failure to use promptly a tip-off about the racist murder from an informant.Reuse content