Here are some examples of how it's used:
* "I know you're excited, but zip your lips! We don't want to spoil the surprise."
* "That's a secret, so zip your lips about it."
* "He just couldn't zip his lips about what happened at the party."
The imagery of zipping your lips like a zipper evokes the idea of a sudden and complete closure of the mouth, preventing any further words from escaping.