The League One club's written request for a judicial review of the decision to grant the Hammers sole tenancy of the stadium was turned down last month.
But Hearn will now attempt to state his case at an oral hearing and is "confident" of a successful outcome.
A club statement read: "Orient would like to confirm that it has renewed its application for permission for a judicial review against the London Legacy Development Corporation in respect of their decision to deny the club Olympic Stadium tenancy.
"The club believe that in refusing permission, the judge erred in his decision on reviewing the papers, and we are therefore opting to debate the issues at an oral hearing where we are confident that permission will be granted."
West Ham were declared anchor tenants in March and are due to move into the stadium in August 2016.
But Hearn argues the move, to within a mile and a half of Orient's Brisbane Road ground, will have an adverse effect on the League One club's attendances.