Lees-Galloway said there was "a wall of silence" around the issue.
The surprising news of Thiel's Kiwi citizenship, first broken by the Herald yesterday, drew international attention with the New York Times, Mashable, Gizmodo and the Daily Mail noting the development.
Lees-Galloway said another wealthy North American import - film director James Cameron - had drawn considerable notice when living in New Zealand, raising questions over why Thiel didn't attract attention if he was living here.
"I can't imagine someone of Thiel's stature and wealth and not being noticed for five years, it just doesn't seem very likely," he said.
Lees-Galloway said he had lodged written questions in Parliament with Minister of Internal Affairs Peter Dunne seeking to know when Thiel was granted citizenship, under what grounds and whether the venture capitalist billionaire was a resident for tax purposes.
The Herald understands, due to the Parliamentary break, the questions will be required to be answered by February 15.
According to the Department of Internal Affairs website, citizenship requires people to have lived in New Zealand for most of the past five years, or have been born in New Zealand, or have New Zealand parents.
Filings to the Companies Office, requiring directors to provide their residential address, have Thiel only list United States addresses. Thiel is widely reported to have been born in Frankfurt, Germany, to German parents who emigrated to the United States when he was an infant.
An alternate path to the above requires the Minister of Immigration to personally sign off and agree that granting the individual citizenship "would be in the public interest because of exceptional circumstances of a humanitarian or other nature".
Thiel's ties to New Zealand are mainly financial, having invested around $50 million over the last decade in accountancy software company Xero and the New Zealand Venture Investment Fund.
The Ministry of Immigration, which handles residency applications - usually a precursor for citizenship - declined to provide any information about the Thiel case.
"Immigration New Zealand said that for privacy reasons it could make no comment," a spokeswoman said.
Questions sent yesterday to representative of Thiel were answered by Jeremiah Hall of Torch Communications. "I'll be back in touch if we have any comment," he said.
No further correspondence has been forthcoming.