I realize there are already several similar questions on this topic, but many of them are from older version of SQLite which did not fully support EF 6 as far as I am aware.
I finally got it too work
I'm using : EF 6.1.3 http://www.microsoft.com/en-us/download/details.aspx?id=40762 and System.Data.SQLite 1.0.96.0 sqlite-netFx451-setup-bundle-x86-2013-1.0.96.0.exe
I followed the description written in: Database first create entity framework 6.1.1 model using system.data.sqlite 1.0.93 (in this description a nuget package of entity framwork is installed -i did it too)
For the app.config file i used these fixes: https://stackoverflow.com/a/24324212/885349 (written by tomexou)
Finally SQLite Connector wasn't shown in the ADO.Net Entity Data Model Mapper
The missing link was the \bin folder. I had to set the "Copy Local" = true setting for following dlls:
Only for completeness - added through Nuget and also in \bin folder
And the SQLite Connection was shown...