Let's say that they are broke or poor and do not have any money (I don't know, this is just hypothetical). LW would use his own discretion to predict whether a payout from litigation is higher than the cost he would have to pay spending time and energy on the case. He could conceivably sue and split the award with the Rs as long as it covers the legal fees he would have charged them to begin with. Or, he could be an altruist and do the case for free (pro bono). I guess it depends on his own motivation for threatening to sue. It could be personal, or it could be at the behest of the Rs.
Agree with the part about his motivation. We can't know that. Most such cases are taken on contingency by attorneys, with the attorney or his/her firm taking a third or more of any settlement or judgment.
Problem for Lin is, I don't see CBS settling when they can get more publicity for finally breaking the case completely open by deposing the killer of JonBenet Ramsey. And once Burke is deposed and it's established that he agreed to do a national TV interview before the airing of the CBS special, the case would probably be tossed by the court.
For a somewhat analogous, if not totally on-point situation, see Terry Hobbs v. Natalie Pasdar. Terry Hobbs was the stepfather of West Memphis murder victim Steve Branch and Natalie Pasdar is from the Dixie Chicks. Natalie mentioned at Free the West Memphis 3 Rally a number of years ago that Hobbs was a more likely suspect than the WM3. Hobbs sued, hoping for a huge pay day. His deposition was a disaster for him and ultimately helpful for young men in prison. And because Hobbs admitted doing interviews about the case, the Court dismissed his claim as he was deemed a limited public figure and was unable to establish actual malice on the part of Pasdar. (He managed to make himself look like a very good suspect in his deposition).
CBS knows what they did and they are clearly okay with it.
Over to you, Lin and Burke...