@Rousette he doesn’t need to “avoid service of the lawsuit” as he is demonstrably not in the New York State jurisdiction and therefore can’t be validly served with the claim. He or his lawyers will doubtless have been sent a copy as a courtesy, but that cannot count as service to mean you are subject to the court’s jurisdiction, as it does not operate extraterritorially.
There is a difference between not submitting to the jurisdiction and not presenting a defence. In the first case you are essentially saying that “the court the claimant has chosen is the wrong court to hear this claim, and it has no jurisdiction over me”. You then take no steps at all in the process. This also means Andrew can argue an abuse of process by the claimant, not least because normally a defendant will not have concurrent criminal and civil exposure against them as the risk of personal prejudice is so high. There is a very high chance if Andrew were to take any steps in the NY lawsuit that meant he actually went to NY he’d instantly be arrested by the FBI, because why wouldn’t they, if he lands in their lap like that? It’s far harder for them to make up a case for an extradition or even compel an interview, which they notably haven’t done yet.
Obviously it’s a decision for the Prince and his advisers to take, but I’d be telling him to decline to submit to the NY court’s jurisdiction, tell Ms Guiffre that if she thought she could prove her case, come and do so in a UK court, which is the proper forum for this, and no further comment other than to deny her allegations. Any default judgment in the US can then be dismissed as an abuse of process in an unfair proceeding which hasn’t heard from the defendant, and any monetary award won’t be enforceable against him in the UK in any event. From his perspective, I don’t think that’s a terrible outcome?