Unless he told them something when the cameras were off . . . technically he did not lie, but he also did not tell them the truth either - under immunity I understand that one can not take the fifth. That’s the whole idea of immunity - unless he can later convince them later that to answer their questions was akin to a death sentence.
Amazingly, the FBI didn’t record or video the interviews, that came out.
With no grand jury, it then follows that there were no search warrants, no subpoenas, no covert recording. The first investigation was designed for the outset to be a cover up.
If they were videos or recorded after immunity was offered we don’t know. I would tend to think all the parties involved know he won’t live to testify in court or before congress -it would make sense to record it.
Presumably, he was offered immunity, because he was taking the 5th.