I would assume LE already has those phone records.
From a legal POV for the civil case I can see the argument being made by the defendants. They aren't being sued for being the ones that brought harm to her. They are being sued as people that should've taken better care of her so that harm didn't come to her when they let her leave their apartment complex. So phone calls, 134 days prior, and 134 days after, will take some spinning to make that relevant to the civil trial.
It's certainly (potentially) relevant to the criminal case and as a way to find out what happened (or might've happened). But the civil case has already been formed. One of the problems is, we all know(greatly assume) it is a fishing expedition. I don't think many of us believe the parents really think that JR watched LS walk out the door. They are simply using 5N's words to create a case that they hope will force them to slip up in questioning or point fingers to avoid a loss at trial.
I don't recall wording of the civil case to point to 5N as the potential cause of her demise anyway or any type of conspiracy to hide what really happened. So that will limit the evidence they can hope to independently get their hands on somewhat.
At the moment I'm having a hard time thinking of a reason those phone calls would be relevant to the narrow terms of what I recall the civil case to be about. Same for the academic records.
I think you're probably right about this. As much as I'd love for this information to be more available/available for the Spierer's, I don't think the civil suit will make that possible. There is a chance that the spierer's lawyer(s) could make a compelling argument for why the records are fair game, I can't think of what that argument could be but I really hope they get the answers they're looking for.