Supporters of a dishonest leader are mostly well aware of the dishonesty (pity the few victims that actually fall for it, because they're most likely to be the eventual casualties of a catastrophic resolution). For them, the lies function as a shibboleth which allows mutual recognition and cooperation through the pretence of a shared counterfactual.
An amusing example is when people complain about 'virtue signaling' - almost everyone engages in this, but because the word virtue has moral connotations it is projected onto people who make moral arguments and superficially appears consonant with and a critique of their behavior, when actually the underlying purpose of the complaint is for people who ostensibly object to virtue signaling to recognize and team up with each other by shared recognition of an in-joke. That is to say, pejorative use of the term 'virtue signaling' is an instance of covert virtue signaling.
An amusing example is when people complain about 'virtue signaling' - almost everyone engages in this, but because the word virtue has moral connotations it is projected onto people who make moral arguments and superficially appears consonant with and a critique of their behavior, when actually the underlying purpose of the complaint is for people who ostensibly object to virtue signaling to recognize and team up with each other by shared recognition of an in-joke. That is to say, pejorative use of the term 'virtue signaling' is an instance of covert virtue signaling.