A lock icon next to a Snapchat Story means it is a Private Story. The creator handpicked a specific group of friends to see it, and you are on that list! It is just Snapchat's way of letting you know the content isn't visible to all of their followers.
Basically, a lock icon on a Snapchat Story means it is a Private Story. If you see the story and the lock, it means you are one of the people who the person sharing the story has allowed to see it.
