Does not register a service worker that controls page and start_url

Registering a service worker is the first step towards enabling key Progressive Web App (PWA) features:

Works offline
Supports push notifications
Can be installed to the device

Learn more in the Service workers and the Cache Storage API post.

Browser compatibility

All major browsers support service workers. See Browser compatibility.

How the Lighthouse service worker audit fails

Lighthouse flags pages that don't register a service worker:

Lighthouse audit showing site doesn't register a service worker

Lighthouse checks if the Chrome Remote Debugging Protocol returns a service worker version. If it doesn't, the audit fails.

How to register a service worker

Success: Workbox is the recommended approach for adding service workers to websites because it automates a lot of boilerplate, makes it easier to follow best practices, and prevents subtle bugs that are common when using the low-level ServiceWorker API directly.

Registering a service worker involves only a few lines of code, but the only reason you'd use a service worker is to make it possible to implement one of the PWA features outlined above. Actually implementing those features requires more work:

To learn how to cache files for offline use, see the What is network reliability and how do you measure it? post.
To learn how to make your app installable, see the Make it installable codelab.
To learn how to enable push notifications, see Google's Adding Push Notifications to a Web App.