Attach a Value Set to a Lookup Table

Wondering if anybody knows if it is possible to attach an existing value set to a lookup table?
The business has the need to maintain a list of organizations that is queried by an external web app to apply certain business rules to.

However, we want to use an existing value set of active organizations for the business to select from.

We have thought about other methods such as user tables, DFF and value sets, but the business does not have access.

Any help would be greatly appreciated.

Thanks!

Mike