"It is ordered that the administrator of the centre shall forthwith administer to all persons accommodated in the centre be afforded their rights under section 42 of the constitution," Justice Canning said.
Presiding over the human rights division of the National Court, Justice Canning said the standing of Mr Namah to bring the case still needed to be determined, as his rights were not directly affected.
But in rejecting the interim injunction application, Justice Canning said there were serious questions to be answered.
"However, the questions of ultimate success are tempered by questions of whether the plaintiff has sufficient interest in the matter."
Justice Canning also said he did not think the interests of justice would be served in granting the interim injunction order.
"I do not see any injustice to the plaintiff or any other persons, including the asylum seekers presently at Lombrum or those who might imminently be transferred there, that would result from a refusal of the interim injunction," he said.
"I can by contrast see that the defendants would reasonably perceive an injustice if the court were to, without being fully satisfied that something unconstitutional or unlawful had occurred, to injunction arrangements that had been entered into in good faith by two independent governments.
"The plaintiff appears to be seeking to enforce the human rights of asylum seekers, but does not name who they are and has made no attempt to join them in the proceedings."
Mr Namah's lawyer, Loani Henao, said on Wednesday afternoon he had received orders from his client to enjoin the asylum seekers in the matter.
However, he said two previous requests to enter the facility had been denied.
The government of PNG has filed a motion to dismiss the proceedings, arguing the National Court does not have the authority to deal with the constitutional questions raised by the case.
The court is expected to resume on Thursday afternoon.