It seems as if they may be aiming to get some sort of evidence that the initial call that kicked this off came into Rexburg PD, either directly by KW or by AZ police on behalf of KW. If I am right about that, it could be that the defense may try to argue that KW had no right to initiate a welfare check and thus these charges must be dismissed because they derive from a person they believe has no right to initiate a welfare check. That will fall on its face, if that is their aim. Anyone can contact law enforcement about any other person to initiate a welfare check and so long as law enforcement has a reasonable belief that there is good reason to conduct a welfare check they will do so. Law enforcement is under no obligation to investigate the caller to learn of the caller's motives - if any.
I think that there is a chance that the defense might argue that Lori lied because she didn't want KW to know where JJ is. However, the law is that law enforcement cannot tell anyone (including KW) where JJ is once they know and he has been seen physically by law enforcement and Lori (actually everyone) is expected to be fully aware and understanding of all laws i.e. ignorance of the law is not an excuse - especially the laws that are beneficial, rather than detrimental, to her in that situation.
It is entirely possible that the defense argument will be that law enforcement, and the State of Idaho, are acting as conspirators in order to take JJ. I half expect some kind of conspiracy nutjob accusation wherein law enforcement is conspiring to take children to give to pedophile rings which is a popular conspiracy theory on the conspiracy sites (they really, really, believe that kind of stuff).
The defense will get some of the stuff they are asking for. I doubt that they will get unredacted recordings or notes where there is any discussion of potential crimes she hasn't been charged with that are, or were, under investigation. Based on the wording it seems very possible that what they request also includes tips submitted by the public.
I wonder whether her attorney will have anything to say today.