I'm going to throw a spanner in the works and suggest that none of them were effective liars. To my mind, an effective liar would have gotten away with it, and come away largely scot-free at the end of the tale. But as we know, all of them met a grisly death! And I think there's a lesson in that.
However, since lmp did not allow "none of the above" as an option, I humbly suggest that Gollum was the most effective, but not in the way he intended. He deceived Frodo into taking the Pass of Cirith Ungol, making out that it was relatively safe, with ill intent. Had Frodo not taken this way, he would never have been able to make it to Mount Doom. Gollum's deception in leading Frodo and Sam that way, and his treachery in reclaiming the Ring in the Sammath Naur led to the destruction of the Ring and the fall of Sauron. Effective!
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But Gwindor answered: 'The doom lies in yourself, not in your name'.
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