Anything that's not already publicly available and is turned over w/o a court order they can probably be sued over.
FWIW I don't think the SoSs should turn over jack to this BS 'investigation'. If you look at who Trump's put on it and is in charge it's becoming pretty obvious that it's a RW ploy to work towards further voter suppression, etc so IMO if this bunch want the public records they can hunt them down themselves. Why should our state tax dollars go towards aiding and abetting this 'witch hunt' crap along with what looks like could be an attempt to attack our constitutional right to vote.
I would think that if the voter lists have previously been sold to various organizations and political parties, it would legally be a problem to refuse them now.