Lorenz had the strongest motive. Why?

Imagine this: The father rapes his daughter. Then, out of fear that the town would accuse them of incest (because she is pregnant and has no husband on top of the prior rumors in the town that the family being incests), he and his insufferable wife force their daughter to approach another man, namely the neighbor (Lorenz), and get him to have sex with her. This way, they can avoid the witch hunt of the town and claim the baby is from Lorenz, so they are not accused of being an incestuous family. The girl approaches Lorenz, seduces him, and gets intimate with him. But she is already pregnant from her father, so she can't get doubly pregnant. Nevertheless, the child is born, and they act like he (the child) is from Lorenz. But as time passes, Lorenz realizes that the child is not his, as he does not resemble his facial features. Or perhaps the girl confesses to him. Why? Because if he is the father, then he might further ask to have sex with her more, as she is his girlfriend. Or he might be pressuring her to confess why the child does not look like him. One way or another, she and her family force him out. He already served his purpose. But that doesn't stop him there. Being forced out and angry at the family, he starts sneaking into their house at night and listening to them from the attic. He hears them talking about the matter and learns that he is being played.

He rejects the child's paternity. Perhaps he starts spreading rumors in town regarding the family being incestuous. In any case, the family wants him silenced. Perhaps she starts having sex with him again as a bribe. Then magically, he accepts paternity of the child. The problem is that as time passes, she starts alienating him again. Now he can't spread rumors that "the child is not mine" anymore because he already accepted paternity. People wouldn't believe him. The family gets even greedier and wants him to pay child support. That pisses him off.

1. They used him as a decoy in a humiliating way.

2. The fact that the family is incestuous and disgusting.

3. The fact that he has to pay child support for a kid who is a product of a disgusting father-daughter relationship.

Combine all of these facts—that's the motive.

But that doesn't answer how; how did he murder everybody?

He starts sneaking into the house like before, but this time it's different. He sneaks into the house to plan their murder. He uses a train to travel to the city center. He buys magazines and cigarettes to pass time while spying on the family from their attic. He probably loses a magazine once and the family finds it.

But there's a problem: He doesn't want to kill the maid as she has nothing to do with "the disgusting family." So he starts making noises, knocks on her door, tries to play ghost so he can spook the maid into running off so then he can murder the family in peace. It works—the maid runs away due to alleged "ghosts."

He plans the murder and kills the entire "disgusting" family. He spends a week in the house cleaning up; only God knows who was killed where exactly.

The unfortunate thing is that there was a new maid there for just one day; Lorenz probably didn't even know she was there after all... He had to kill her because she presumably witnessed the murders.

Otherwise, Lorenz "seems" like a "decent" person as he leaves cash on the table after staying in their house for a week to imply that "he is not a thief."

Though why did he kill the little girl? She had nothing to do with all that "filth"... Who knows—maybe he saw her grandfather raping her too? Perhaps he thought it would be better to kill her than let her live with that "filth". Plus she is a witness. Who knows.

But I doubt that Lorenz was alone in this act; he had a family of his own. You can't just disappear for murdering people for a week without your family noticing it—especially in such rural places.

His sons probably helped him in committing these killings.

After all, "the evil family" not only made fools of their father but also took his money via child support payments.