The Green in Petyr's spiritual portrait represents his dominant personality trait, his preference for logic over emotion. In Introverts, the dominant trait is directed inwardly, and spiritual portraits use a long horizontal line to represent this. He demonstrates this trait in the way he is calm while treating people very coldly, even to the point of betraying them completely.
The Blue in Petyr's spiritual portrait represents his auxiliary personality trait, his fairly strong preference for ideas over facts. In Introverts, the auxiliary trait is directed outwardly, and spiritual portraits use a vertical line to represent this, because it is more evident than the dominant function. He demonstrates this trait in the way he builds his entire life around an idea - the idea of him sitting on the Iron Throne.
While Petyr was growing up with the three Tully siblings, Lysa fell in love with him, but he did not love her in return. Instead, Petyr's heart belonged to Catelyn.
But then Catelyn wound up marrying Ned Stark, moving to Winterfell, and breaking Petyr's heart — assuming he had one. Ultimately the infatuations driving this triangle of unrequited love prove to be fatal, largely due to Petyr's devious machinations.
A Man With a Big Idea
The Blue in Petyr Baelish's spiritual portrait shows he has a fairly strong preference for ideas over facts. This preference is quite obvious in a conversation he has with Cersei Lannister about her father Tywin before the midpoint of the series:
Cersei Lannister: My father's a practical man. He appreciates facts.
Lord Baelish: Myself, I often find them a hinderance.
— From And Now His Watch Is Ended, Season 3, Episode 4 of Game of Thrones (2013).
This preference makes Petyr rather unique in Westeros, where most of the people are — of necessity — pragmatic and down-to-earth.
Because he owns a brothel, at first it seems Lord Baelish is interested in money. In a conversation with Varys he makes it clear he has a single, highly specific ambition:
Chaos isn't a pit. Chaos is a ladder. Many who try to climb it fail and never get to try again. The fall breaks them. And some are given a chance to climb, but they refuse. They cling to the realm or the Gods or love. Illusions. Only the ladder is real. The climb is all there is.
— Petyr Baelish in The Climb, Season 3, Episode 6 of Game of Thrones (2013).
Whether he missed the raven's memo or just doesn't care is a moot point. Like all the other players, Petyr ultimately learns that, as Cersei so famously said,
when you play the game of thrones, you win or you die.
While the Blue in Petyr Baelish's spiritual portrait shows he has the ability to strategize, the Green in his image represents his ability to logically devise specific tactics for obtaining his goal.
If you want to get to the Eyrie, you need to go through the Bloody Gate. It doesn't matter how large your army is, if you attack this gate, you do it on this road, [which exists in a ravine with cliffs on both sides, guarded by sentinels on the cliffs] three men abreast, and get slaughtered like goats. The first Lords of the Vale didn't have much, but they had these mountains and they knew how to use them. And the fortress they built here has never been overcome. Not once in 1,000 years. Know your strengths, use them wisely, and one man can be worth 10,000.
— Petyr Baelish in First of His Name, Season 4, Episode 5 of Game of Thrones (2014).
For one thing, it's remarkable how Petyr likes to think and speak in terms of powers of ten. With a cast containing many characters who prefer logic to emotion, this may well be the first real use of mathematics on the show.
More significantly, it's quite clear he believes he can combine his intelligence with a proclivity for devious acts to become the equal of — and, in his dreams, perhaps even superior to — the high-born of Westeros.
Petyr the Player
Petyr's devious machinations help him advance, but only up to a point. He ultimately meets his match when he tangles with the
children of House Stark.
Lord Petyr Baelish: Anything I can do for you, Brandon, you need only ask.
Bran Stark: [Holding the dagger that Petyr gave him.] Do you know who this belonged to?
Baelish: No. That very question was what started the War of the Five Kings. In a way, that dagger made you what you are today. Forced from your home, driven out to the wilds beyond the Wall. I imagine you've seen things most men wouldn't believe. [Hands him the scabard for the dagger.] To go through all of that and make your way home again, only to find such chaos in the world, I can only imagine -
Bran: Chaos is a ladder. [A door opens and Meera enters.]
Baelish: [Chuckles softly.] I'm sorry to have disturbed you, Lord Stark.
Bran: I'm not Lord Stark. [Baelish leaves.]
— From The Spoils of War, Season 7, Episode 4 of Game of Thrones (2017).
When it comes to specifics — mood and overall mise-en-scene, number of characters involved, manner of death, trial or the lack thereof, and so on — Petyr's final scene shares very little with the one in which Olenna Tyrell meets her end. However, both scenes are excellent and well worth re-watching several times.
If anything, though, most people would surely agree that seeing Baelish meet his demise is more satisfying than seeing Olenna's final moments. This is only natural, of course, because his patronizing and creepy character is by far much more despicable than Olenna's self-centered — yet overall rather entertaining — abrasiveness.