lie vs fabricate. When to use which one in what situation?

As a commenter suggested, when we use fabricate in the context of deception,¹ we imply that some effort went into inventing or producing something disingenuous, either a story or an artifact, like a fake document. If you simply said 'no' when you knew full well that the truth demanded 'yes', it is unlikely anyone would say that you 'fabricated' an answer. But everyone would agree that you lied.

^{1In other contexts, fabricate can mean simply to invent, create, or to construct, manufacture; specifically, to construct from diverse and usually standardized parts (Merriam-Webster).}

On a formal grammatical side, fabricate is a transitive verb, while lie is most commonly intransitive.² Normally, we simply say that e.g. he lied, or else we add a preposition phrase and say that he lied about [something]. In contrast, we say that he fabricated [something], as in he fabricated a story.

^{2Much more rarely, lie can also function as a transitive verb. Here is an example from Merriam-Webster: He lied his way out of trouble.}

As far as the meaning, fabricate means 'To concoct in order to deceive' (fabricated a convincing excuse) (American Heritage); 'To "make up"; to frame or invent (a legend, lie, etc.); to forge (a document)' (Numerous lies, fabricated by the priests..were already in circulation; If any person..wilfully fabricate in whole or in part,..any voting paper.) (OED).

As for lie and similar words, Merriam-Webster has the following useful discussion:

lie, prevaricate, equivocate, palter, fib mean to tell an untruth. lie is the blunt term, imputing dishonesty. // lied about where he had been // prevaricate softens the bluntness of lie by implying quibbling or confusing the issue. // during the hearings the witness did his best to prevaricate // equivocate implies using words having more than one sense so as to seem to say one thing but intend another. // equivocated endlessly in an attempt to mislead her inquisitors // palter implies making unreliable statements of fact or intention or insincere promises. // a swindler paltering with his investors // fib applies to a telling of a trivial untruth. // fibbed about the price of the new suit //

To fabricate originally was to make, and this is still one of the meanings. One can fabricate a story, a piece of cloth, or a car. To fabricate a story is to make it up, and the fabricated story is false because the truth does not need to be made up. To fabricate evidence is to make it (instead of discovering it. See https://en.m.wiktionary.org/wiki/fabricate

To lie is to tell a false statement intending it to be taken as the truth. If you tell your fabricated story as the truth then you have lied. If you present your fabricated evidence as real evidence you have also lied, and your research will be suspect even if your results are actually true.

To call a statement a fabrication is to say it was made up, and is therefore a lie instead of being the truth. These days the word is more often used in this sense than with the earlier meaning.