"Hide" a document if someone else is already viewing it?

Our legal department came to us with a funny request.  They have a document that the vendor has copyrighted, and the legal department insists if one person is viewing it, that absolutely no one else can view that document.

I can't think of any way we can do that in Sharepoint (2013), without real coding.  I tried thinking of ways we could do this with workflows, or just with Flow, but can't think of anything.   I can't figure out a way to give everyone permissions to view it, and then when someone else opens the document that it automatically takes away view from everyone else, and then when the person closes the document it automatically puts those permissions back in place.

The problem is that the whole legal department needs access to this document, it's just that it's licenses for one user at a time, and the vendor is evidently serious about absolutely only one user viewing it at a time.  I'm not sure how they would be able to ever tell that more than one user had viewed it at a time, but Legal wants to make sure we enforce that.

Any ideas on how we could make this work?

Thanks.

Ted