Wasn't the shooter over 18? Why would his parents be concerned about lawsuits? They're not legally responsible for him anymore.
If they were legally responsible for him, it appears they clearly would've kept him in mental health care.
I just don't see how they're liable once he's passed 18 and he was allowed by the state (again, no one stopped him) to discontinue treatment.
Granted, the parents are failure by themselves -- this however sounds more like a failure of the State's mental health resources to properly identify him as an 'at risk' individual.
I’d say if they knew he was nuts and funded the gun purchases then yes they are liable.