What fallacy is committed when one argues that a conclusion is false simply because the person arguing it has lied before?

Question

For example, suppose I were to make the claim:

President Trump says climate change is false. President Trump has lied before; therefore, climate change is true.

Answer 1

Here is the argument:

President Trump says climate change is false. President Trump has lied before; therefore, climate change is true.

Irving Copi divides informal fallacies into those of relevance and those of ambiguity. We may start by deciding which one of these two this argument falls under.

A fallacy of ambiguity is one "whose formulations contain ambiguous words or phrases" (page 120). Nothing seems ambiguous in this argument. Fallacies of relevance, on the other hand, have premises that are "logically irrelevant to, and therefore incapable of establishing the truth of, their conclusions" (page 98-9) If this is fallacious, it is likely a fallacy of relevance.

What one might conclude from the premise that President Trump has lied before is that he might be lying now. However, that alternate conclusion to what needs to be shown that climate change is true has not been explicitly stated.

One name that might work for this argument is ignoratio elenchi or irrelevant conclusion since the premises are, as the name of the fallacy suggests, irrelevant to the conclusion. This may seem to be an obvious choice, but there may be better choices.

Something else may be going on here. The conclusion being drawn is climate change is true. So the person making this argument is using Trump to gain support for climate change among those who do not agree with Trump. In this context, one might consider this a red herring.

Douglas Walton, in trying to find a way to distinguish between ignoratio elenchi and red herring, describes a red herring as follows: (page 2)

The second, commonly known as red herring, is the fallacy of switching the topic of the discussion to some different issue that may be highly entertaining and diverting to the audience, distracting its attention form the real issue to be discussed.

Given this description of red herring, it seems to be a better fit. The real issue is deciding whether climate change is true or false. The entertainment is bringing up Trump among those opposed to him to divert their attention from the real issue and thereby gain support for the conclusion.

The question in the OP's title, however, is more general:

What fallacy is committed when one argues that a conclusion is false simply because the person arguing it has lied before?

If the choice in this case is between ignoratio elenchi and red herring the better choice may still be red herring. Claiming that someone lies arouses an emotional appeal against that person in the audience. Walton calls this a "strategic diversion" (page 22). The audience may be distracted (entertained) more than misled to some "wrong conclusion" that is irrelevant to the real conclusion that needs to be proved.

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Copi, I. M. Introduction to Logic. Sixth Edition. Macmillian (1983)

Walton, D. (2004). Classification of fallacies of relevance. Informal Logic, 24(1). https://www.dougwalton.ca/papers%20in%20pdf/04fall_rel.pdf

Answer 2

Such an defense, asserting that the proponent has lied before, is a form of ad hominem argument: the truth or falsehood of an assertion is said to rest on who the advocate is or on things they have done in the past, and not on the content of the assertion itself. See Logically fallacious > Ad hominem (abusive).

Here, the denial of climate change might prove true. But its truth will not rest on any one person's reputation.

The fallacy here might also be the inverse of an appeal to authority. See Logically fallacious > Appeal to false authority.