Post-Truth Office Politics

The company I work for appointed a new CTO a while back. He plays post-truth office politics. With this I mean he makes up narratives to support his agenda without any regard for the truth. He doesn't care whether what he is saying is true, or whether it contradicts what he said two weeks ago or what he will say two weeks in the future.

Most of the old timers have left the company. New employees last less than a year before they resign. The remaining long term employees are just sitting tight, not speaking up, not pointing out the lies, not correcting mistakes made by new employees, not peer reviewing code by the new employees, etc. The group-think seems to be to not get involved, not associate with any of the new software that is being written and just wait for it all to implode.

I have found out the business has been very unhappy for a few months because they need a report that apparently can't be produced. I coded a similar report a few years ago so I was surprised. I looked into it and found that the CTO deleted the raw data about a year ago. He is now claiming that the system I coded was never able to do this kind of reports.

For a number of reasons, resigning is not an option for me.

What is a good way to deal with this situation? Both the concrete issue with this report and the wider problem of constant lies.