Offizieller Kommentar
Using two different computers actually makes it kind of easy... connect USB-B to the Lenovo, configure the DJM-S9 Setting Utility to have the MIX (REC OUT) as one of the outputs, then install the ASIO plugin for OBS. Select the S9 as the source, and select the pair of outputs that matches the pair you chose for the REC OUT.
Done!