The 'alfa' lawsuit says exactly that the 'GOP' hired out Fusion GPS who hired Steele to do the research. They were looking into the russia connection and such. They dropped the info after Trump won the primary. The Dems later picked it up.
The Free Beacon might not have started the dossier, but it was started by affiliates from the GOP. That has been put forth in court.
Everything I read says Steele wasn’t hired until after FB pulled out. Have no idea what lawsuit you are referring to. And, in our current legal system, just because something is filed in a court proceeding does not give it credence as truth.