LineageOS 16.0 is officially supported on the Fairphone 2 by the LineageOS community. There’s nothing more stable with regular security updates.
Nightly builds are just the way the LineageOS community operates, there’s no “stable” label.
15.1 was nightly builds only, too.
Where did you get the idea LineageOS would include Google Apps and services?
As @lklaus mentioned, you can just install them via https://opengapps.org.