Aren't we talking about the New York Times here? They can print whatever headlines they choose to print.

There wouldn't be anything going on in the lawsuit that's worth a headline.

If they wanted to use their "ink by the barrel" power to engage in reprisals against Trump, they certainly can. But writing about the lawsuit would be a horrible way to do it. If you wanted to write a headline about Trump's involvement with Epstein, write an article about that - and put a headline over it. "Trump's Close Ties With Epstein Cause Political Problems" is a better headline than "Judge Delays Ruling on Routine Motion for Protective Order."

Unless the NYT was actually going to get any useful documents out of this, it's not worth spinning wheels in a discovery process - and they're not going to get any documents out of it. And the process of not getting any documents is not likely to generate anything worth writing about, because Trump's lawyers probably aren't going to have to do anything dodgy to avoid those disclosures.