I have an update to share on this subject. Since the time this discussion was opened, a new "custom Bricks" feature has been added to Arduino App Lab:
That feature does not allow you to customize the contents of the primary Docker container in which the App's Python script runs. However, it does allow you to run additional custom containers, which the Python script can interface with. This is actually how some of the official Bricks provided by Arduino work already.
Unfortunately we haven't published documentation for the custom Bricks feature yet, but the documentation team have already produced a draft of the documentation, which you can access here in the documentation source repository:
Note that the brick_compose.yaml file in the custom Brick is a Docker compose file, so the documentation provided by Docker will also be applicable:
You might be able to find an existing Docker image published on an image registry (e.g., Docker Hub that provides all the capabilities you require. Alternatively, you can create your own custom image. If you create a custom image, you should note that (at least currently), you must manage this independently. Since Arduino App Lab takes care of managing the App's containers for the user, you might expect that it would handle building the container from the image source automagically, but unfortunately this is not supported. The "gotcha" is that it will actually build the container the first time you start an App with a custom Brick that references a local image source. However, afterwards you will run into a confusing situation where changes you make to the image source don't have any effect on the behavior of the Brick, due to the fact that Arduino App Lab / Arduino App CLI doesn't rebuild the container as needed (arduino/arduino-app-cli#389) and will instead simply continue to use the container it built from the previous version of the image source on the first run.
I'm happy to provide some assistance with managing containers built from a custom image source if you end up going that route (you can find some information on the subject in the related discussion starting here).
Here are some examples of custom Bricks that use a dedicated container: