Anonymous
I am afraid that using Grouped field on multi-value lookup field won't work in the current release. I would recommend that we try to use the built-in feature of Complex Category in qDiscussionView to achieve the desired behavior and display.
The Complex Category feature is designed to function similarly to those in Notes application with nested category, but can also be used to accomplish the design here. It requires a bit of setup but can work as conveniently as using lookup field for the Category grouping field described above.
First, drop the qDiscussionView web part on the page and configure it to connect to the underlying discussion board.
Next, create a Category field as Multiple line of text field. This will be used to hold multiple values of category.
Next, from qDiscussionView web part context menu, click "Create Complex Category Index List" to create a list that help maintain the values of Category created. This would be equivalent to your lookup list. The drawback is that you would have to fill this list first but we have something to help you with that – will be explained later.
QuickApps Complex Category feature work in concert with qDiscussionView and qListForm, where we will use qListForm to manage discussion entry, including the Category field we created earlier. From qDiscussionView web part page, launch different form page for create, update and display form page, hide the OOTB list form and add qListForm. Configure each qListForm to the proper form mode (new, update or display and etc.), include the fields (the same as included in OOTB form or your preference) but make sure you include Category field and configure this field in ezEdit screen to be "Complex Category" field. You will need to set up the Complex Category Index List (the one you created at the step 3 above).
After this is done, you will notice that qListForm will allow you to create new Category (or nested sub category as well but we do not need that in this case). You can create as many category as you want as top level category or only create the category the current discussion item belongs to. But all category created will be shared among instances of the discussion item when using qListForm configured this way. After you created the category, you can check it and save the item, this will effectively put this discussion item under this category. You can select multiple categories – works the same way as using Category as lookup field allowing multiple values.
Back to qDiscussionView, you would include Category field in the Display Fields property, configure it as "Complex Category" field and specifying the URL and name to the Complex Category Index List you created at step 3.
Finally you desired result should be rendered. In addtion, you can argument your category right inside the edit/create discussion thread page (where qListForm is configured to work with the Category field as Complex Category) by adding more category, by selecting multiple values or de-selecting value.