Compelling others to repeat your lies is a well-established interrogation technique that is designed to break the spirit of those being interrogated. It's also a means to assert dominance over subordinates.
Cialdini and various social psychologists argue that when individuals can be coerced into abandoning their integrity by being compelled to repeat untruths they can then be bound to the coercive force by a need for consistency, mixed with shame and complicity.
Jacob T. Levy's piece about Authoritarianism and Post-Truth Politics highlighted this: [The] great analysts of truth and speech under totalitarianism—George Orwell, Hannah Arendt, Vaclav Havel—can help us recognize this kind of lie for what it is. Sometimes—often—a leader with authoritarian tendencies will lie in order to make others repeat his lie both as a way to demonstrate and strengthen his power over them.
Saying something obviously untrue, and making your subordinates repeat it with a straight face in their own voice, is a particularly startling display of power over them. It’s something that was endemic to totalitarianism.