You are going to have to let go of this lying issue. It is just a distraction and it takes you nowhere.
The other side gets to take its position on the facts and the law. The defense gets to tell it the way they see it, and make their contentions based on their understandings, inferences, deductions, memories, conclusions, assumptions, and intentions. You get to disagree and proffer an altogether different version.
Someone -- not the EEOC -- will eventually try to figure out which version is closer to the ever-unknowable "truth." Or, the parties will mutually decide to let the truth-finding mission slide and instead resolve the dispute without bridging that chasm.
In all events, the EEOC does not intend to conduct the kind of searing search for THE TRUTH that you want. Neither will the EEOC do anything about it if the agency is convinced by one party's factual contentions over another. In fact, no agency of any branch of government is going to investigate or consider your contention of perjury, and no penalties are going to be imposed based on the statements made by the defense. If you want to complain, complain to your lawyer -- over a cup of coffee. The usual and regular penalty for obvious lies is that the liar doesn't win the case. But sometimes even that penalty is beyond reach.
You will be issued a right to sue, as soon as you request one or whenever the EEOC gets around to it if you don't request one. It will not even mention lying, nor will it make any findings of credibility or lack thereof.
Sorry; this is the reality of the system.
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You should produce the New Jersey Department of Labor notice of determination to the EEOC to counter your employer's claim that you quit. You can also get a transcript of the Department of Labor hearing and produce it, if you think it will be helpful to you. However, even if the EEOC finds in your favor, it is unlikely that it will find that your employer committed perjury. Your employer is entitled to take the position that you quit, even if that is not what happened from your point of view or that of the Department of Labor.
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Good luck with getting a federal prosecutor
to file perjury charges against your ex-bosses.
Employee "rights" are WAY down on the criminal
food chain chart. NOW . . . if you had lied against
some billionaire's (owner) interests . . . you'd be
hiring one of us AVVO attorneys to defend you
in court. -----Like the lady said . . . give up the
perjury angle. Technically you're right but they've
changed the rules for employees. ----Good luck.
THIS ANSWER IS PURELY FOR ACADEMIC DISCUSSION ONLY AND DOES NOT CONSTITUTE ANY TYPE OF LEGAL ADVICE OR LEGAL REPRESENTATION.