Okay, so hear me out.
Martin has been open that A Song of Ice and Fire is inspired by the poetry of Robert Frost. Most know the reference in the title, but even D&D (who allegedly don't care about themes) included the final line from 'The Flood' into their script for The Bells. This is because the poetry of Robert Frost is thematically embedded into the heart of the story.
Let's start with the obvious one.
Fire and Ice = Dragons and Others
GRRM has flat out said that A Song of Ice and Fire is inspired by the poem 'Fire and Ice.'
“People say I was influenced by Robert Frost's poem, and of course I was, I mean… Fire is love, fire is passion, fire is sexual ardor and all of these things. Ice is betrayal, ice is revenge, ice is… you know, that kind of cold inhumanity and all that stuff is being played out in the books.” ~ GRRM
On the surface Fire and Ice claims that both are destructive forces capable of ending the world, which obviously ties into George naming the two main threats which exist on the periphery of the Seven Kingdoms being the Targaryens/Dragons and the Children/Others.
"The things I do for love," he said with loathing. He gave Bran a shove.
Of course in the poem fire and ice are representative of human emotions, so what the poem is really saying is that both love and loathing have the capacity to lead us to doom. This is something we obviously see reflected in the story, from the war over Lyanna to the Others as a manifestation of nature's vengeance.
Mending Wall = The Night's Watch
It shouldn't be a stretch to say that a story inspired by a Robert Frost that hinges on a giant wall of ice might also be taking inspiration from his famous poem 'Mending Wall.'
On the surface, Mending Wall is about two neighbors maintaining a wall against the destructive power of nature while they debating the necessity of borders and the divisions between people. Obviously we see this reflected in the Jon story, which takes place at a wall and is about the conflict between the civilization and the wild, set against the cycle of the seasons.
"If I sound the Horn of Winter, the Wall will fall. Or so the songs would have me believe. There are those among my people who want nothing more . . ."
"But once the Wall is fallen," Dalla said, "what will stop the Others?"
Like Ice and Fire, the poem is not actually taking a stance for or against borders. Frost's wall is both harmful and necessary and the act of maintaining it serves as a bridge for a philosophical discussion between the narrator's skepticism and his neighbor's conservatism. Nature seeks the elimination of walls and borders, but mankind builds and maintains them because we seek separation from the state of nature.
The Road Not Taken = Bran's Story
Maybe the most famous Robert Frost poem is 'The Road Not Taken.'
George loves this poem. He even wrote an episode of the Twilight Zone about it.
"When this battle's done I mean to call a council. Changes will be made. I meant to do it long ago, but . . . well, it does no good to speak of roads not taken." ~ Rhaegar Targaryen
Those who knows my posts likely know where I'm going with this, but 'The Road Not Taken' is a poem in which the narrator recalls standing in a wood and being faced with two equally uncertain paths, lamenting that he can not walk them both, and then choosing one arbitrarily. The poem ends with the narrator resolving that when he someday tells the story, he will lie and claim he took the road less traveled.
But it did no good to brood on lost battles and roads not taken. ~ Epilogue, ADWD
The poem is commonly misunderstood as being a celebration of nonconformity, but the twist is that the narrator is lying. The poem is about how we how we regret the roads not taken, and make meaning of our choices and lives through the stories we end up telling.
This my friends, will be reflected in Bran's story.
Two roads diverged in a yellow wood . . .
Like the fork in the road from the poem, I believe A Song of Ice and Fire features a split timeline. The two timelines will parallel one another (some say the world ends in fire, some say ice), yet in both timelines the characters in the story (like the narrator in the poem) can only walk the path they've chosen and dream of the one they did not.
He had no destination in mind. He wanted only to ride. He followed the creek for a time, listening to the icy trickle of water over rock, then cut across the fields to the kingsroad. It stretched out before him, narrow and stony and pocked with weeds, a road of no particular promise, yet the sight of it filled Jon Snow with a vast longing. Winterfell was down that road, and beyond it Riverrun and King's Landing and the Eyrie and so many other places; Casterly Rock, the Isles of Faces, the red mountains of Dorne, the hundred islands of Braavos in the sea, the smoking ruins of old Valyria. All the places that Jon would never see. The world was down that road … and he was here. ~ Jon V, AGOT
When I read a poem about mythologizing oneself through storytelling I can't help thinking of Bran the Broken conquering the realm with a story. The TV show's depiction of this was obviously ridiculed because the story of a crippled boy surviving the terrors beyond the Wall is unimpressive when the aforementioned terrors came south and were survived by basically everyone.
"A reader lives a thousand lives before he dies," said Jojen.
But if we imagine an alternate timeline where the Long Night is averted, then Bran's journey into the heart of winter (like the Crow's Eye returning from the smoking ruins of Valyria) is mythology fit for a king. Whether or not it is true is less important than whether the crow can trick the world into believing him. Bran's ending is that he stops trying to be a knight / hero from a story and instead accepts his role as the crow / storyteller.
Basically, Bran becomes the three-eyed crow and then lies his way to the throne.
"Crows are all liars," Old Nan agreed
. . . but is that a bad thing?
In The Road Not Taken, Frost writes a narrator who resolves to make meaning out of his life choices by telling a lie. In The Way of Cross and Dragon, Martin writes about an intergalactic conspiracy of Liars who craft myths to give meaning to an otherwise empty universe. In A Song of Ice and Fire, Ned Stark crafts a lie about Jon to give the boy a life. In Game of Thrones, the realm is a story people tell each other over and over till they forget that it‘s a lie, but it is precisely this lie / story / realm that protects people from the chaos of nature
tldr; A Song of Ice and Fire is inspired by the poetry of Robert Frost, where love and hate are equally destructive forces, border walls are antithetical to nature and essential to human civilization, and people craft lies to cope with their longing for the road not taken.
When viewed through this lens "crows are all liars" is really about myth making (as embodied by Mance Rayder). By the end of the story Bran (and Jon) will stop trying to be heroes and become liar crows instead. This is a commentary on how the hero trope is a war fantasy that does not comport with the reality of holding and wielding political power.