LineageOS looks online for the entered number, but that is not their business.
1. Switch of the forward lookup, the people lookup and the reverse lookup (Telephone-App - three points in the search field - Settings - phone number lookup).
The question whether you are connected to the internet should not be googles decission:
1. Replace Google captive portal check with [Kuketz](https://www.kuketz-blog.de/android-captive-portal-check-204-http-antwort-von-captiveportal-kuketz-de/). Therefore, connect your Fairphone with your computer and execute following adb commands:
```
adb shell 'settings put global captive_portal_http_url "http://captiveportal.kuketz.de"'
adb shell 'settings put global captive_portal_https_url "https://captiveportal.kuketz.de"'
adb shell 'settings put global captive_portal_fallback_url "http://captiveportal.kuketz.de"'
adb shell 'settings put global captive_portal_other_fallback_urls "http://captiveportal.kuketz.de"'
```
In order to test the settings, if they were correctly adopted, you can type in:
`adb shell 'settings get global captive_portal_https_url'`