What does "Nothing screens violence except lie, and the only way lies can hold out is by violence" mean?

It means that violence and lying support and are highly related.

Explanation:

Violence and lying are not beneficial things that do not generate good results and therefore are not supported by anything but yourself in a strongly established relationship. Violence is often protected only by lying, which stands in favor of violence by showing certain events in which it can be beneficial, justifiable. In this way the violence is established, making this lie to endure forever among us.

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