Superannuation fund managers legally have to transfer the money within 30 days of receiving the correct paperwork.
Lawson contacted the NZ Herald to say AMP Australia was refusing to follow the rules and release her money.
"It seems to be astonishing that one of Australia's largest fund managers and iconic institutions, which has a subsidiary in New Zealand offering KiwiSaver funds, is not willing to do this," Lawson said.
Other people have also contacted the Herald reporting the same issue with their Australian super providers.
AMP yesterday announced it would be enabling full portability between Australia and New Zealand for its superannuation customers.
"AMP has a significant presence in both Australia and New Zealand so our priority is to get this in place in both countries as soon as we can," said spokeswoman Amanda Wallace.
"We are waiting for further clarity on some aspects of the regulation in Australia, but we have started work on the Australian side of our portability program."
Wallace said AMP could not say when the service would be available because it needed time to put its systems in place. Also, New Zealand KiwiSaver providers were still not ready yet to receive the money.
"We are working on it. It's a very complex programme and it does take time."
She "hoped" portability would be available sooner than the end of next year.
AMP would also be contacting Lawson personally to talk about the matter, Wallace said.
Australian regulation around portability was released only recently which meant the industry had been caught off guard.
While New Zealand approved the legislation in September 2010, it took until the end of May for Australia to firm up its side of the deal - just one month out from its introduction date.
That caught out providers on both sides of the Tasman, leaving them scrambling to put their systems in place.
KiwiSaver providers are working on having portability fully enabled but industry sources say it could take up to six months for them to be ready.
In Australia, not only is the industry playing catch up on super portability but it is also busy dealing with a range of other new rules to have been implemented this month.
Wallace said KiwiSaver providers had been given "a head start" because the legislation was approved earlier in New Zealand.
Superannuation portability allows people to consolidate their retirement savings in their country of residence and avoid paying unnecessary fees and charges on multiple accounts.
Bringing it home
* Kiwis can apply to transfer money in Australian superannuation schemes to their KiwiSaver scheme.
* Home country laws will apply to the transferred money.
* Retirement savings transferred from Australia into a New Zealand KiwiSaver scheme can be withdrawn when members reach the age of 60 if they meet certain criteria.
* KiwiSaver savings transferred to Australian schemes can be withdrawn when members reach 65.