Late to the party and you’ve already gotten great responses from @Procrustus and @Ann_Hedonia. But just to add to their excellent information, this is how it goes down, at least where I clerked:
If a juror is found to have lied during voir dire prior to the end of case presentation, the juror is excused and replaced with an alternate. The lying juror is sometimes prosecuted for this, but rarely.
If a juror is found to have lied after deliberations have begun but before a verdict is taken and the judge determines that other jurors haven’t been tainted, the lying juror is excused and replaced with an alternate. The liar is prosecuted for perjury at the discretion of the prosecutor.
If a juror is found to have lied after deliberations have begun but before a verdict is taken and the judge determines that other jurors have been tainted, the lying juror is excused and a smart judge will immediately declare a mistrial and start again. Never. Ever. Take. A. Verdict. From. A. Tainted. Jury. (I saw this error happen once in a huge case. It was immensely consequential and tragic.) The juror will probably be prosecuted for perjury.
If a juror is found to have lied after the verdict is taken but the jury still convicts, then the defendant has a great big issue on appeal and will probably win a new trial. The DA may decide to try the case a second time or they may be more inclined to settle, because the appeals process takes time. By the time a new trial is ordered, witnesses may be out of reach of a subpoena, victims much older, everyone’s memories are less clear or maybe critical witnesses have died. It’s an awful situation for a prosecutor.
The most awful situation is if the juror lied during voir dire and as a result, the defendant is found not guilty as a result of those lies. If the verdict has been taken, then yes, double jeopardy attaches and the defendant goes free. The juror will almost certainly be prosecuted to the full extent of the law for perjury. Happily, I never saw this one happen in my career.
But I have experienced some of the other situations. It’s never a good thing when a juror lies to get on a jury for whatever reason.
I see a very strict gag order in Individual One’s near future. Let him violate it once (what are the chances?), and it’ll be home detention for him, with limited access to internet and phone. Trump is giving the judges in his cases every reason to issue tight restrictions on his pre-trial speech.