Hi Andreas,
Your dockerfile approach is resulting in a version of JupyterLab that is more recent than the version that binder currently uses. If you launch JupyterLab from the current example, you’ll note the version that comes up from there lacks the little icons in the bottom left corner you see when you launch yours.
If you want to use a more recent version there is a way to start it off upon launch with a specific notebook directly. In fact the bottom of the JupyterLab Binder example points a more recent version of JupyterLab that runs on Binder. The JupyterLab Demo repo includes in the binder directory a file spelling out a workspace in json. The last line of the postBuild in that directory tells jupyterlab to import that workspace and so when it starts you launch with a specific notebook on the left and a panel with a webpage form the documentation open on the right. Workspaces can be made more simpler. I have one that currently just opens the index page at this repo. And there too postBuild is used to import it.
The simplest way I have found to make the workspace is to launch into a repo Binder and get the view the way I want and then in a terminal window run jupyter lab workspaces export . But I think this only works when you have a workspace already set-up, at least when launching on Binder. I just tried it in yours after bring up a notebook and everything is blank, confirming my view that expoert doesn’t help initially. The longer way that seems to work no matter what get is to first get the path the the workspaces by running in a terminal jupyter lab path. Then cd to the Workspaces directory , look at the contents using ls, and cat labworkspace.. file. Then I copy that to my new workspace.json file and edit the id info right near the end to just read '"id": "/lab".
However, this is all where methods other than a Dockerfile is being used by docker2repo to make the build form the repo. I think that besides making the json file, you can probably add an equivalent line to your Dockerfile like the one that is used in postBuild (or sometimes I have seen the same line in start) pointing at that json to import it. The caveat being that use of a Dockerfile is kind of the most adventurous path, and so YMMV.