Which formal fallacy(s) cover "he who has told a lie once can never tell the truth"?

Questions like this are why object to the way critical thinking is taught,

An argument is a conclusion drawn from at least one premise. Hence, an argument always contains at least 2 statements, never less.

A fallacy is a kind of argument.

A formal fallacy is a kind of fallacy that is unreliable because of its form only.

I can construct both a formally valid and a formally fallacious argument that reaches the statement in question as its conclusion.

If anyone tells a single lie then they will always lie

He told me a lie

therefore he will always tell me lies

this is entirely valid. its called modes ponens

If anyone tells a single lie then they will always lie

He has always lied

therefore he told me a lie just now

This is invalid (formally fallacious) It's called affirming the consequent

I am aware that many teachers of critical thinking will give their students one statement like the one in this question, and ask them to identify some fallacy or other. This in my estimation is simply stupid. It shows that the teacher doesn't know the meaning of the words that they are using. It is like asking someone what kind of mammal an organism is when the organism does not have a heart or kidney. Mammals require hearts and kidneys and arguments require at least two statements.

You can of course make up some argument or other that has the statement as the conclusion thus demonstrating that you know how to reason fallaciously, and this is usually the aim of the exercise.(More's the pity)

Outside of necessary statements (all bachelors are unmarried males) there are no statements that are always true or always false.

for example, "he who has told a lie once can never tell the truth"

Imagine an island inhabited by two groups. The first group always lies and the second group always tells the truth. So, if you find yourself there if someone lies to you once then you know that he will always lie to you.

In this context the statement is true. Meanwhile, on planet earth just because someone lies to you once is no reason to think that they will always lie. You don't need to find a name for it there are several good ways to show that this is true. But none of the ways of proof are formal. If anything of the form

If something happens once it will always happen that way

is always false. then the laws of physics are unreliable. and just because someone is a male today they may not be tomorrow and you can never flip a coin twice in row and get heads both times.

Non sequitur. The second does not necessarily follow from the first.

It is scientifically fallacious also; first define 'lie' without using context and Perspective.

The First Law of Soul Dynamics tells us that;

"For every Perspective, there is an equal and opposite Perspective!"

What you se as a lie, another will see as true.

Everything is true!

"All statements are true in some sense, false in some sense, meaningless in some sense, true and false in some sense, true and meaningless in some sense, false and meaningless in some sense, and true and false and meaningless in some sense." -Robert Anton Wilson

We are unique every moment! One moment that we might 'lie' is not a prognostication that every other moment will be similar.

That is just ignorance, an appeal to ignorance!

No. I tell lies to my consumers every time i bypass to artwork, infront of my colleagues and with the understanding and approval of my boss. in case you disapprove then you definitely tell me a thank you to calm an 80 4 365 days previous widow who's hysterical approximately getting domicile because of the fact she had a infant the day gone by and her husband does not understand a thank you to look after it. My reaction to her is that she is staying with us to get better, she would be able to no longer be any sturdy to the infant if she is going domicile and collapses and that i've got sent a nurse to help her husband.

Yes, all the way down. I saw it at once!

I'm thinking it's equivocation, the quality of consistency being grafted onto the established situation of being once a liar. For the liar to be consistent, he would need a philosophical, religious or political platform in which lying (at least to a particular audience) is required. In your example, the definition of "liar" is switched in midstream from "one who has told a lie" to "one who cannot but tell lies."

Latin? I'll leave that to a friend of long ago whose T-shirt read, "QUIDQUID LATINE DICTUM SIT ALTUM VIDITUR."

I think a word has been left out at the end. "Convincingly".

I like your picture of stacked turtles. Is that a Dr. Seuss reference?

Edit: Hahaha. Thanks for sharing.