It seems perfectly natural and appropriate that Marlow should lie to Kurtz's fiancee when she asks him to tell her Kurtz's last words. Heart of Darkness was published over a hundred years ago. In those days women were treated with more deference and delicacy than they are in our modern times. There was a whole code of etiquette involved in men's relations with women. For example, men would either remove their hats or at least tip their hats when addressing ladies. Men would all stand up in a restaurant if a woman rose to leave the table, and they would stand up again when she returned and remain standing until she was seated. Some vestiges of such formal manners are still to be seen in public today, but times are changing, not necessarily for the better. There were, of course, many subjects that men could not discuss in the presence of ladies, and certain words they would never ever use. It is hard to imagine Marlow blurting out the truth that Kurtz's last words were "The horror! The horror!" Marlow was sufficiently quick-witted to come up with the perfect lie, which was that Kurtz's last words were his intended's name. The following quote from Heart of Darkness is illustrative:
It’s queer how out of touch with truth women are. They live in a world of their own, and there had never been anything like it, and never can be. It is too beautiful altogether, and if they were to set it up it would go to pieces before the first sunset. Some confounded fact we men have been living contentedly with ever since the day of creation would start up and knock the whole thing over.
At the end of the story, Marlow has been through a literal hell on Earth, and has witnessed the very worst of humanity as brutally shown by Kurtz. Marlow is disillusioned and tired; he wants nothing more than to forget the entire journey, but he knows that all of it, especially Kurtz's final words -- "The horror! The horror!" -- will stay with him forever. On meeting Kurtz's Intended, a nice young woman with no idea of Kurtz's terrible deeds, Marlow is torn between the desire to be truthful -- he has seen too many lies recently -- and the need to allow her a last piece of Kurtz to remember.
"'His last word -- to live with,' she murmured. 'Don't you understand I loved him -- I loved him -- I loved him!'
"I pulled myself together and spoke slowly.
"'The last word he pronounced was -- your name.'"
(Conrad, Heart of Darkness, gutenberg.org)
It is possible that Marlow sees The Intended as the last good part of Kurtz, the last thing that he affected in a positive way, and he can't bear to destroy her with the truth about Kurtz. To spare her the terrible burden that he has been forced into, Marlow lies; his small lie gives her piece, and so the horrors that Kurtz created ended with some small good deed. Now The Intended can go on with her life, feeling that a great man loved her passionately, and she will never need to know what really happened.
We have to engage in some conjecture to answer this question. As such, several possible answers present themselves.
There may be a sense that the darkness Marlow found in Kurtz somehow belongs in the Congo and should remain there. To tell Kurtz fiance about his actual end would be to release this darkness into the wider world.
We might also wonder if Marlow saw a purposeful/intentional and intact innocence in the fiance and did not want to destroy that innocence.
Rather than explain the truth of Kurtz's life in Africa, Marlow decides not to disillusion her. He returns some of Kurtz's things to her—some letters and a pamphlet he had written—and tells her that Kurtz's last word was her name. (eNotes)
Another possibility is that Marlow may feel that explaining Kurtz dissolution and his turn to evil is too much to explain. Marlow had to go all the way up the Congo River to discover what he does about Kurtz. The fiance has not made the same journey and so may not be prepared to understand the things that Marlow has seen.
Marlow has two possible paths here - to answer truthfully or to lie to The Intended. The first option would be in line with what he learned from his experience with Kurtz. It is clear that Marlow respects Kurtz's truthfulness both in his words and in his actions, even if he is also slightly repelled by the same aspects of the man. However, Marlow is no longer with Kurtz in the middle of the Congo. He is back in Europe, surrounded by individuals who enjoy kind outward appearances, even at the expense of the reality. As such, perhaps Marlow is motivated to fit into his surroundings and therefore chooses to lie to The Intended to ease her heart, just as any other European would do.
Toward the end of Conrad's "Heart of Darkness", Kurtz lies dying on the steamboat as Marlow attempts to bring him back to civilization. Kurtz’s final words are “The horror!The horror!”When Marlow returns to England, he meets various acquaintances of Kurtz, many of whom glorify the deceased adventurer’s character and what he might have aspired to had he lived. Marlow also meets Kurtz’s fiancée, who believes in Kurtz’s nobility and is devoted to the mythology of Kurtz as the great Christian do-gooder who has gone into the heart of darkness to transform a savage civilization. She is committed to the idea that Kurtz’s memory must be preserved because of his remarkable nobility.D. The Kurtz she imagines does not exist at all. The real man is virtually the opposite, taking a native mistress, and killing others at will. He is a man who (paraphrasing Marlow) had kicked himself loose from the Earth, a man who became a god in the land, an embodiment of appetite and savage un-restraint. When Marlow encounters Kurtz’s fiancée, he knows all these terrible things about Kurtz. He especially remembers Kurtz’s last words. Marlow is horrified by the fiancée’s deluded notions, but she coerces Marlow into reassuring her of Kurtz’s nobility. Such coercion is a recurring drama in Conrad, and it shows his insight into the idea that conversation itself is political and coercive, not necessarily a mutual experience. The fiancée asks Marlow Kurtz’s final words. Marlow yearns to answer truthfully. His whole narration has been about truth and the difficulty of reaching it. But as much as Marlow hates lies (as he tells readers earlier), he tells the fiancée what she wants to hear—that Kurtz’s last words were her name. In an ironic twist, however, the fiancée believes wholeheartedly in Kurtz’s nobility and thus completely believes and embraces the rationale for Western imperialism. The ending implies, in a wonderful and disturbing way, that Marlow’slie speaks a kind of truth. No wonder the fiancée is confined, in the story, to a sepulcher and is, for the reader, a kind of horror herself.
One thing to be noticed during Marlow's conversation with Kurtz's intended is that the lady's tone is as formidable as Kurtz. Marlow sees a spectacular similarity between Kurtz and his fiancee. In fact at one point he says "I saw them together- I heard them together". The intended is shown to to have such a powerful personality that Marlow is forced to agree with whatever she says even if he believes quite the opposite. She is firm in her tone and has a note of conviction when she says about Kurtz "It was impossible to know him and not to admire him, was it? Now and then she silences Marlow into an appalled dumbness with her pride of knowing Kurtz the best. Her menacing possessiveness with Kurtz is similar to Kurtz hysterical outburst when he says "My intended, my station, my career...". His intended at the end goes on to say "Ah, but i believed in him more than anyone on this earth- more than his own mother, more than himself. He needed me!me! i would have treasured every sigh. every word, every sign, every glance".Hearing this Marlow is more frightened than sympathetic and therefore lies to the intended that her name was the last word spoken by Kurtz. Marlow is unable to tell the truth because its too dark and would collapse her world. To say that this was an act of idealistic motivation and benevolence would be wrong rather the lie becomes an unavoidable necessity. Marlow could dare to speak something which the intended would not have liked to hear. She commands the same authority that Kurtz had once held and which no one had dared to oppose.
There is no easy answer to this, but the general assumption is that Marlow wishes to hide Kurt's real character from her, his "heart of darkness" as it were, and so lies. He supplants Kurtz's last words "The horror! The horrow! with the lie that he last spoke her name, something she instantly deems as appropriate and predicted. The political aura revolving around this tale mirrors that of the British Raj, or invasion of India, in which soldier's stories, upon returning, were often changed in light of what they had done and not the natives themselves. Thus, when Marlow returns, he chooses to bury the truth of Kurtz's madness in the Congo and return with a lie which meets certain societal ideals of the Victorian age. By ending in this manner, Conrad is bridging the gap between the closing Victorian era and Modernism, two modes of thinking which straddle the fence between idealism and realism which are symbolically drawn from the lie he utters and the dramatic irony with which the reader views the truth.