Hi Ves,
If you mentioned Syphon are you using Mac correct ? If yes you can output your video to Syphon in a Mac and then use this problem to stream this Syphon output to other computer NDISyphon | VIDVOX Documentation. This program will get your Syphon output and will stream it as NDI in your Network and this can be them captured in other computer.
Using this approach you can add then output of Rekordbox Video or Lyric into Resolume form instance. I am using this approach in some projects and also to integrate Rekordbox and Resolume (Rekorbox -> Shyphon -> NDISyphon -> Resolume adding NDI Source).
If you are using Windows you have to check Spout and them the same approach can work.
Sérgio