Zion opened in 2002 and Mrs Busch took it over in 2006 after raising money to pay off the park's debts.
The park's troubles have been long-running and included the death of South African keeper Dalu Mncube, who was mauled by an endangered white tiger in 2009. The cat was destroyed following the attack.
Stuart Hamlett, owner of Rotorua's lion park, Paradise Valley Springs, said he wouldn't be able to take in any of the lions.
"It's very sad but we definitely can't take any. We don't have the room and we have our own breeding programme going. The logistics of taking these cats just makes it impossible for us to be involved."
He estimated it would take the equivalent of more than four horses a week to feed 36 lions.
The Rotorua pride numbers nine and they can't be caged with other lions. They would not be able to be housed together because of their predatory and protective natures, he said.
"You can't mix them. It would be dynamic. It's a long, slow process. I'm very sorry for the lions but our pride is settled.
"[Zion] have dug themselves a hole but sadly it's not an option for us to take any. I doubt if anyone else can take them either."
A few years ago, the Rotorua park gave Mr Busch one of its female lions named Scarlet. Her name was changed and Mr Hamlett said he isn't sure if she was still at Zion.
It's not the first time a New Zealand lion park has closed its gates. An Auckland park was closed years ago under similar circumstances.
Meanwhile, Evgeny Orlov, lawyer for the park's operator, Mrs Busch, has said the bank's application was surprising and unfair. He said the lions were wildlife and not the property of receivers. There were places all over the world where the animals could go, he said.
- Additional reporting APNZ
