Rightly or wrongly, I was never much perturbed by the 'Liar' paradox in philosophy, which, like so much else, first appeared in classical Greece. I always felt that paradox would rarely, if ever, trouble us since liars don't normally declare themselves to be lying. But there is more to think about.
On browsing through an account by R. L. Kirkham of recent analyses of 'liar' senstences, like 'This sentence is false', 'This sentence is false or neither true nor false', 'This sentence is not true', etc., it suddenly dawned on me that the philosophers were missing the main point. All the analysis and argument was about whether paradoxes or self-contradictions can be shown to be not true, and if so how. This was what is meant by 'solving' them.
But that is not what is happening when someone is lying. The liar is indeed saying something which (he or she believes) is not true, but is trying to pass off as the truth, i.e., deceive. The last thing a liar will do is say his or her statements are not true, which is just what he or she does not want others to know, and so will employ the same grammar and syntax as someone telling the truth. Liars sometimes contradict themselves, but that's when they get caught out (usually with different statements). This applies regardless of whether the case is the more usual one where lying is manipulative and self-regarding, or whether the intention is to protect or comfort someone else with a 'white lie'.
Accordingly, efforts to solve paradox or contradiction do not affect liars. Kant was at least right that dealing with liars depends on moral regulation, not logical analysis.