So I got a reply from Support (I translated the reply from Dutch):
Google build this camera and phone swipe behavior on the Lockscreen into Android 5.1, and this behavior cannot be changed.
This is a choice from Google we have no influence over.
It may be possible to do this with certain apps, but you’ll have to search in Google Play Store for that.
Or you can ask in our Forum.
I searched in the Google Play Store, and found several Apps.
I chose Echo.
Note that the default Lockscreen should be disabled when using this App.
Edit: Hmm, Echo has no options for widgets as well, it’s just another Lockscreen as is.
I like it by the way, but it’s not really a solution for the TS.