Yep Law's ship had one but the second one is ??? because of the way the prompt was worded. We didn't thread out anything besides that first one so there is an option for handwaving a second if and only if there is one fragment unaccounted for and no one else was planning to thread it. ICly Law would have made sure all of them were picked up but idk where other boats/parties are with that.

Curufin had one for sure as well, idk if Jill's prompt meant they also got a chance at a second or what.

Lab-wise Law isn't lurking any more than usual but he's being public about turning them over to the lab because he wants the entirety of the city to act as a fail-safe to guarantee that all fragments are accounted for and no one can hide anything. He's not pushing Kate and Alphys to do anything but he fully understands, after touching one, that they're probably going to have to go Sorrow's route and he's not going to complain. Anything to get a Door.