There may be a way by conversion to fisheye, then to equirectangular. Daniel might advise on the mathematics of it or whether any of his plugins could be used in the process.
@AndriiShramko is nothing like 'render' on resolume, since is a live purpose tool. But is not a deal to capture his output. If you allready have your content formated as equirectangular inside resolume (you know can use the ffgl or the shader commented before for that), your best bet is syphon recorder (or fraps on win) to 'render it'.
Can you elaborate a little bit more about your needs?