Do they know they’re lying, or are they so locked into their closed loop that they really don’t know what’s real and what’s not?

Six of one, half a dozen of the other.

In all seriousness, though, I would say it’s the latter, at least for the average nutter. They’re so tightly enclosed in their alternate reality bubble that they legitimately think everything they hear and read is true. The people manipulating the nutters, however, damn well know better.