Bosses at an event management firm say they are owed about Â£18 000.
A judge on Monday said he would consider their winding-up application on June 12
Tax officials said a debt owed to them had been paid.
A lawyer representing Orient said Â£1million was due to be injected into the club soon.
The judge, Registrar Nicholas Briggs, had analysed the case at a Bankruptcy and Companies Court hearing in London.
Fans said after the hearing that Orient were still in "mortal danger"
Kelly Kaye, 39, a fan for 32 years, said: "It would be good if the club could be sold.
"I would like it to go to somebody who can actually take care of it and look after it properly.
"We've got a great history."
Source : PA