Assume that Party A has brought a civil lawsuit against Party B. Assume further that Party A has issued a document preservation demand upon Party B covering all documents in Party B's possession, custody and control pertaining to their dispute. Can Party B honor a request by a non-party to the lawsuit for production of a copy of a document covered by the preservation demand?
Based on other questions you have posted, I assume you refer to some jurisdiction in the U.S.
Can Party B honor a request by a non-party to the lawsuit for production of a copy of a document covered by the preservation demand?
Generally speaking, it can (absent any reasonable privacy issues, non-disclosure agreements, or judicial prohibitions), but does not have to.
One exception is where party B is an entity subject to provisions such as the Freedom Of Information Act and the records at issue are within scope of FOIA. That applies regardless of whether the records sought are in Party A's list for litigation hold.
Other than that, the non-party may sue Party B for injunctive relief so as to compel the production of documents. However, this would require the non-party to persuade the court that some entitlement to that production. The entitlement could be in equity, by law (such as FOIA if it applies to Party B), or potentially conductive to --or determining of-- other type of relief in the future.