#If you need to justify it, the easiest sell is information security.

Chances are you deal with information that is sensitive to the company and you may need to deal with this information in paper form from time to time. Therefore, a lock on the storage cabinet is a requirement, as you have a responsibility to keep this information safe and make sure only the relevant people can get access to these documents, with the consequences of not being able to fulfill those responsibilities usually ranging from dire to business-ending.

This is something your superiors should be able to easily understand and make some sort of provisions for.