The option you have can be found here jss.sitecore.com/.../layoutservice-rendering-contents
If you want the data from the 3rd party model as a component, in a placeholder, place it on he page in the Experience editor, or add it on the standard values. than creating a "Rendering Contents Resolver" is a good option. you can also cache it, if possible handy if this 3rd party controller is slow, perhaps you can rewrite the logic from the controller in the Content Resolver, calling a controller (calling a controller from code seems like a lot of overhead to me)
Or do you want the 3rd party model data on every request?