The late daughter of Elvis Presley fired off 2 emails to the director four months prior to January -- when she suffered cardiac arrest and passed away -- in which she pled with her to stop down on her feature and reconsider putting it out ... which she didn't, of course.

According to Variety, which obtained the correspondence, LMP called Coppola's script "shockingly vengeful and contemptuous" ... and went on to slam the way Elvis is portrayed.

She writes, "My father only comes across as a predator and manipulative. As his daughter, I don’t read this and see any of my father in this character. I don’t read this and see my mother’s perspective of my father. I read this and see your shockingly vengeful and contemptuous perspective and I don’t understand why?"

Lisa added, "I will be forced to be in a position where I will have to openly say how I feel about the film and go against you, my mother and this film publicly."

In response, Coppola answered ... "I hope that when you see the final film you will feel differently, and understand I’m taking great care in honoring your mother, while also presenting your father with sensitivity and complexity."

It sounds like Coppola actually toned her movie down compared to the source material it's based on -- Priscilla Presley's 'Elvis and Me' -- which apparently contained even more scandalous stories about Elvis courting the very young PP at the time ... something that has come under a lot of scrutiny in the years following his own famous death.

As we reported ... Lisa's cry for the film to be shut down echoes what Elvis' own estate said about the film as it was being worked on -- which, at the time, called it a travesty. Priscilla herself, however, was very much on board from day one ... speaking to the fracture here.