Forest Litigation Reform Act of 2023 This bill sets forth provisions regarding legal challenges to federal forest management activities on land suitable for timber production. The bill revises the standard of review for a court considering a request for injunctive relief applicable to an agency's qualified forest management activity. Specifically, a court must balance the impact to the ecosystem of undertaking the agency action against not undertaking the agency action. The bill also limits the length of preliminary injunctive relief and stays pending appeal in such cases to 60 days. Additionally, the bill directs the Department of Agriculture, with respect to National Forest System lands, and the Department of the Interior, with respect to public lands, to each establish a discretionary arbitration pilot program as an alternative dispute resolution process for challenges to qualified forest management activities. The bill prohibits amounts from being obligated or expended from the Claims and Judgment Fund and awards to pay any fees or other expenses to any plaintiff related to an action challenging a qualified forest management activity.