I am dubious that LW is going to be able to sue CBS, especially since BR has willingly come forward to do interviews and this officially makes him a public figure.
If he does sue, this is going to backfire even more than the interviews done on Dr Phil. There is a good possibility BR will have to take the stand and answer for the discrepancies of his statements and the statements made by LW and the Rs the last twenty years (like the claim of being in bed the entire night of JBR's murder, then later admitting he got out of bed to play with a toy). He is bringing MORE attention to BR, and MORE attention to the BDI theory. As an outsider looking in, I probably would not have even started reading about this case if BR had not done the interview on Dr Phil. Had BR not done the interview, I probably would have missed the CBS special altogether and read about it in passing somewhere else.
LW is melting down about suing people, but hasn't looked at how his own behavior is making the Rs look bad, especially since he admitted on Dr Phil to using the threat of legal action to get what he wants.