One possible moral could be the importance of truth. Since it's a 'lie monster', the story might be trying to show that lies can be harmful and that we should always strive for truth.
Well, in the 'lds lie monster story', the moral could be multi - faceted. Firstly, it could be about self - awareness. People need to be aware of the lies around them, especially if there's a monster spreading them. Secondly, it could be about the value of integrity. The LDS community, or any community for that matter, should uphold integrity in the face of false information. And finally, it could be about the strength of faith. If the LDS people in the story rely on their faith to combat the lie monster, it shows that faith can be a powerful tool in the battle against falsehood and deception.
The moral could be about the power of a community. If in the story the LDS community comes together to face the lie monster, it shows that when a group unites against falsehood, they can overcome any threat that false information poses. Also, it might imply that lies can be defeated by the collective truth - seeking nature of a community.