A labour inspector analysis of the hours worked by the workers estimated they were underpaid between $5000 and $7000 each, INZ said.
Lam was previously taken to the Employment Relations Authority, which ordered him to pay five workers nearly $37,000 for unpaid wages, minimum wage arrears, public holiday pay, failing to provide individual employment agreements and making deductions from pay.
INZ's acting fraud and compliance manager Dean Blakemore said the employment of unlawful migrant workers would not be tolerated.
"This case shows that the consequences of such behaviour are serious. We will take swift action against any employer who is involved in such activity."
The Ministry of Business, Innovation and Employment was treating this issue as a priority and INZ and labour inspectors' compliance activity was being increased, he said.
"Most employers and most migrant workers are complying with the laws of New Zealand - they are being undermined, and New Zealand's reputation sullied, by some who are breaking the law."