I don't think there would be any legal basis for such a lawsuit. In fact, I don't think the lawsuit by lawyers against the legal review site has any basis -- it is just a bunch of egotistical lawyers who had their feelings hurt and too much time on their hands.
I cannot imagine such a lawsuit even getting filed if the plaintiff has to pay attorney's fees, and I cannot imagine such a lawsuit surviving summary judgment --it would be dismissed after discovery was done.