Myth and narrative are not mutually exclusive terms and they both have multiple senses, so it gets squishy.
Narrative is a text genre. So the text genre of a literary myth is narrative (as opposed to expository or hortatory, for example.) As I pointed out above, myth and narrative are often used interchangeably when talking about the telling of history with an agenda.
I was using the term narrative in the way it is commonly used in sociology or political science, as a way of identifying a person’s framework for understanding the world. For example, my husband enjoys commenting on NPR threads about development work and international politics. It is a common narrative among other commenters that religion is destroying the world and can not be credited with any good. All facts and information are filtered through and made to fit their narrative and serve as further proof that their narrative accurately describes the world. So according to their narrative, I am involved in development work, not because my religion has motivated me to do a good thing and help people, but because I have a white guilt complex I need to feel better about, or I have a secret desire to exploit the poor somehow, or I am a pathetic loser who could not get a real job in the US. You could say this narrative, that religion is destroying the world and no good can be credited to it, is a myth (synonym for lie) and offer a different interpretation of the facts. You wouldn’t really be simply exposing a lie though, you would be offering a different narrative, a different interpretation of information that supports a different story about how the world works and different conclusions about what it means. That kind of thing is not easily reduced to a truth value. You evaluate narratives on a better/worse continuum (not a true/false continuum) based on how well they correspond to and explain reality and how much a person has to manipulate, fabricate, or ignore in order to maintain the narrative’s coherence.
As far as myth and fiction…
I think myth is a kind of origins story (not necessarily purely fiction) that intentionally attempts to communicate insight, truth, and meaning about things that are important to the identity or beliefs of a community. In many ways the way we tell early American history to children is mythic. It is based on real facts and people, but we “mythologize” them to serve our purposes of creating an identity as Americans and to teach our beliefs about freedom, democracy, equality, courage, etc. We leave parts out when they don’t fit the narrative. We fictionalize parts to make them fit better. If several thousand years went by, the story of how American began would probably become even more mythic.
Historical fiction is a story someone makes up to communicate the facts of history in an entertaining way. A mythologized history is a story that tells the facts of history from a certain perspective and with goals of instilling certain beliefs and values.
I don’t draw this big black line between story and truth like it appears you do. There are lots of stories that communicate true things. Sometimes the true things they communicate are facts. Some times the true things they communicate are ideas. You evaluate the value of a story based on what it is claiming to do (entertain, motivate, inform), not strictly on some kind of truth-o-meter that corresponds only to accurate representation of historical facts. Humans use stories for much more than communicating facts. We use them all the time to define ourselves and find meaning in the world.