I know in the private sector if fired you can pretty much lie if ever asked and odds are no one will find out.

Probably different for government jobs. They will know if you've been fired from a government job. And once you are institutionalized as a beauracrat it can be hard to work elsewhere. You would basically be restarting your career from scratch.

And if they know, so what? The mere fact of being fired for doing the right thing will wreck your life?