Miserly, the insurer in this problem, and any litigant in any suit, would most likely want to obtain material that could have a negative effect on its opponent's case. This would include social media postings of remarks or photos that discredit the opposing party's claims.
Lori, or any party whose postings are sought, might argue that complying with such a request would constitute an invasion of privacy. But to effectively assert a right to privacy, a party must have a reasonable expectation of privacy in the particular situation. Even though people often believe that posting in social forums is private, it is probably not reasonable to expect privacy in postings on social media. It might be contended more successfully that such material is not relevant to the case at hand.
And in this problem, in the absence of a showing that any of the posts undermined the plaintiff's claims, the court would most likely deny the defendant's motion. But the court might grant the defendant the right to make the motion again if it could be shown that the material sought is relevant to the case.