Private Cloud subscribers have their own separate database and how the ability to control all of their Lookup Lists. 

Go to the Admin Center and click on the Lookup Configuration link in the Sidebar.

On the Lookup Configuration page click on the Gears Icon to open the Lookup Configuration Select list. Scroll down to the specific Dropdown List that you want to Add/Edit and click the list name.

That will open up the page showing the current values for that list. 

You will see the Add New Record link to create a new value or click the Edit button to change a current value. You cannot delete an existing value since it may already be in use.