It usually indicates that the snap story is private and only accessible to certain people or requires a password or permission to view.
Well, a lock under a snap story typically means it's restricted. Maybe it's for a select group of friends, or it could be set to only be visible to the person who posted it. Sometimes it's because the content is sensitive or personal.
The lock on a snap story basically means it's not for public viewing. It might be because the owner wants to control who sees it, or they might have shared something they only want a limited number of people to access. Could also be for privacy or exclusivity reasons.