Maybe I'm dense or naive, but I don't think there's any precedent for that. A gag order is one thing (and there are certainly places for it), but forcing someone to lie would hopefully violate the First Amendment.
It's strange that chainsaw10 is being downvoted for their comment. From the second link above, "Have courts upheld compelled false speech? No, and the cases on compelled speech have tended to rely on truth as a minimum requirement." That sounds more like there is not precedent to force people to tell explicit lies.
Maybe I'm dense or naive, but I don't think there's any precedent for that. A gag order is one thing (and there are certainly places for it), but forcing someone to lie would hopefully violate the First Amendment.