A little while ago, I argued with a friend of mine over the efficiency of the Chinese government. I admitted he was clearly better informed on the subject than I. At one point, however, he claimed that the Chinese government executed fewer people than the US government. This statement is flat-out wrong; China executes ten times as many people as the US, if not far more. It's a blatant lie. I called him on it, and he copped to it. The outcome is besides the point. Why does it matter that he lied? In this case, it provides weak evidence that the basics of his claim were wrong, that he knew the point he was arguing was, at least on some level, incorrect.
The fact that a person is willing to lie indefensibly in order to support their side of an argument shows that they have put "winning" the argument at the top of their priorities. Furthermore, they've decided, based on the evidence they have available, that lying was a more effective way to advance their argument than telling the truth. While exceptions obviously exist, if you believe that lying to a reasonably intelligent audience is the best way of advancing your claim, this suggests that you know your claim is ill-founded, even if you don't admit this fact to yourself.
Two major exceptions exist. First, the person may simply have no qualms about lying, and may just say anything they think will advance their point, regardless of its veracity. This indicates the speaker should never be trusted on basically any factual claim he makes, though it does not necessarily show self-doubt. Second, the speaker may have little respect for the intelligence of her audience, and believe that the audience is not sophisticated enough for the truth to persuade them. While this may be justified, depending on the audience,1 unless there is good evidence to believe the audience legitimately would not process the truth accurately, this shows the speaker is likely wrong about his central point. However, "the masses are ignorant and should be lead by their betters" is a pretty effective cognitive dissonance resolver, so he may not experience the same self-doubt.
This principle applies in direct proportion to the deception, and in direct proportion to the sophistication of the speaker. An informed person relying on outright lies indicates either an Escher-like mind or a belief in the wrongness of your position. Lesser deception indicates lesser reservations. An uninformed person may well lie to support proposition that a better informed person could support easily with the facts. But, if an apparently informed advocate is resorting lies and deception, it strongly suggests he has little else to work with.
1- This is not necessarily unjustified. Consider a babysitter with a child who walk by a toy store. The babysitter needs to get the child home soon. The child gets excited and starts demanding they go in, and the babysitter says, "We can't, they're closed!" This may be patently false, but, in this case, the truth is very unlikely to convince his audience, even if better solutions may exist.