I think we don't really know why the P's have chosen this particular course of action. They have said they are taking legal action for lots of reasons. Well, they haven't exactly said that although they seem to be tweeting more now and making public statements that way. But at any rate, their attorneys have been speaking for them all along.IMO, the only reason for the lawsuit is to punish BLs parents, because BL himself is beyond punishment. Quite unfair. MOO.
What you suggest is certainly possible. There isn't any way to punish BL. And so his parents may be "stand-ins." And it wouldn't be beyond belief they might think the L's are to blame for what BL did (although the lawsuit against the L's is not for responsibility for GP's death.) It doesn't make sense to me to think parents are responsible for their adult children's actions but some do think that. Maybe the P's do. As @ktm44 noted, surviving family members may feel irrational guilt when a family member is murdered. They may blame themselves even though they shouldn't. And they may also think parents of a murderer must have done something wrong for the murder to have happened. In other words, the L's should feel guilty like the P's may. And all the parents did facilitate the road trip in some way.
The P's may also want answers to why the tragedy happened. (I do not think they want to know facts like GP's date of death. They claim to already know that.) But I don't think they'll get the answers they are seeking. I doubt the L's know what the P's have claimed they know & even if they did, that's not going to tell them why. Looking at BL's suicide note leads me to think no one will ever really know why (beyond the sort of hypotheses discussed here: a toxic relationship plus a long road trip.) And I do think the P's will find the trial pretty taxing. Courtrooms aren't victim-friendly.
JMO