What did I do ?
I installed LocalWP on my Mac Mini, built a website, exported it. Then I installed LocalWP on my MacBook and imported the site.

Now I sync both folders
/Users/Username/Library/Application Support/Local
and
path/to/local/website

using Resilio Sync, which runs automatically in the background.
It is important to run only one Installation at a time ( either Mac Mini or MacBook ) and you have to wait for syncing being completed, before starting LocalWP on the other machine.
With this set up I work for several month now without any problems.