Many parents see what their children are as a reflection of themselves, and to accept that the child they brought into the world and so lovingly and carefully brought up and who until their child is accused has always appeared a loving and caring individual and worthy of admiration- not just to them but a wider circle, is, in fact, an evil murdering monster is beyond their capacity to comprehend and the only possible response is just not to believe it, at least until they have time to go away and completely rethink their child. This could take months or years.
How do you come to terms with the facts that your lovely loving daughter, in whom you have invested so much of your time and emotion, is a serial murderer. Their whole lives have been hollowed out, everything they built their lives upon has been destroyed - and by the object of their devotion herself.
They will proably have to move from somewhere they have lived all their married lives, possibly change their names, because it is distinctive. I think LL will end up murdering her parents by her actions as effetively as she murdered those babies.