"Believable" is a hypothetical judgement - could a reasonable person believe it. It doesn't matter whether you believe it or not, or whether you know it's untrue, the question is whether it's plausible. 

Well, to me this statement is logically OK. To be credible doesn't mean to be true. So a lie can be credible and still be a lie.

Yes, I agree. If we have no foreknowledge of the lie.

But here the speaker knows (i.e., has foreknowledge that) all the statements are lies, as s/he says: "Out of all the lies you told, none is believable." 

Statements (the truth or falsity of which have not been verified or are unknown) are credible.

Lies when known to be lies are never credible. It's a logical impossibility.

If for some cultural language reason you wish to tell me this sentence in French is acceptable I will accept your assertion. But if instead you are insisting that, at least with respect to the English, it's logical, I am sorry but you are wrong.

I might know that what you have said is a lie, but that doesn't mean that everyone knows. I can still have an opinion as to whether the lie is believable to other people.

Yes, true, but the context here does not readily lend itself to the possibility of the presence of other people.

The speaker says "you" so is obviously speaking only to the person(s) who told the lies.

The key point here is that the speaker has foreknowledge of the lies. Once foreknowledge is introduced the statement is not logical.

If instead the speaker said: "Out of all the lies you told, none was ever believable," the context changes. Now the speaker is indicating two things, albeit vaguely: 1) there was a point in time when the lies may not have been known to be lies and appeared credible and 2) all statements are now known to be lies.

But I'm sure Lawless French wants to provide it's students with simple, logical grammar points. Not examples that contain some abstract or tortured meaning

In my understanding, "personne ne" also is a statement about people not in the group, whereas "aucun/e" refers to the people in the group only.

Tous les gosses y vont, mais personne ne prend le train. -- All the guys go there, but no one took the train. (Not even people apart  from the "guys").

Tous les gosses y vont, mais aucun ne prend le train. -- All the guys go there, but none (of them) took the train.

That sounds right to me.

Hi Dragana,

Aucun is singular and functions as the subject of the sentence, hence the verb needs to match the singular and therefore it is "est" and not "sont".

-- Chris (not a native speaker).