SAN FRANCISCO—A heated discovery process continued to play out today in the lawsuit between Waymo and Uber, when a hearing ended with a federal judge ordering Uber to allow a Waymo-chosen expert and attorney to examine Uber’s LiDAR system.

US District Judge Alsup also said he’s likely to order documents to be handed over, beginning with a privilege log. He even suggested that lawyers for Anthony Levandowski, the Uber engineer at the heart of the case, start preparing an emergency appeal motion to challenge him.

Those statements came at the end of a hearing that lasted more than an hour, which mainly focused on arguments over a privilege log—essentially, a list of documents that the defendant, Uber, believes should be withheld from the other side for one reason or another.