Do you need to refresh your memory and go back to the first season of the series?
Beware, SPOILERS! Do not read on if you are not up to date with Game of Thrones
In the last chapter of season 7 of Game of thrones has finally done justice: the Stark sisters have finished with Pinky. That rivalry between Sansa and Arya has given much to talk about in the last chapters and, contrary to what seemed, they have come together to destroy their enemies, the Stark are stronger than ever!
As they say in the chapter, Pinky is sentenced to death for killing Lysa Arryn for conspiring to murder Jon Arryn and for betraying Ned Stark:
"You murdered my aunt, Lysa Arryn, you pushed her through the Moon Gate and you saw her fall ... Before, you conspired to murder Jon Arryn.You gave Lysa Lágrimas de Lys to poison him [ ...] You made my Aunt Lysa send a letter to our parents telling them that it was the Lannister who murdered Jon Arryn when, in fact, it was you.Conflict between the Stark and the Lannister, it was you who started it. [...] You conspired with Cersei Lannister and Joffrey Baratheon to betray our father, Ned Stark.Thanks to your betrayal was imprisoned and then executed for false charges of treason "
You may well remember Meñique's betrayal-after all, it lasted for a whole season-but you may also have forgotten what happened. If you are in the last group, here is a brief summary so that you understand who Jon Arryn is, why Pinky was against Stark and, basically, what the acts that caused him death were.
THAT'S HOW TO PUNISH NED STARK
The story of the series begins when Jon Arryn, the Hand of the king Robert Baratheon dies, and this one proposes to Ned to take its place. After receiving the offer, he receives a secret letter from Lysa Arryn in which he says that the Lannisters have been implicated in Jon's death. Ned decides to investigate his death and a possible plan that would endanger Robert. Now we know that Pinkie was the one who instigated to kill Jon and inform this to Ned.
Pinkie was also to blame for Catelyn kidnapping Tyrion Lannister as revenge for Bran's fall from the tower. It is he who tells him that the dagger that the killer supposedly carried - the one he gave Bran Stark this season - belonged to Tyrion. What causes the first confrontation between both families.
Ned discovers that shortly after the death Jon Arryn, his squire Hugh was named knight, but it does not manage to speak with him, since the Mountain assassinates him in a "tournament accident". After refusing to accept a plan to assassinate Daenerys Targaryen and knowing that there is a conspiracy in Landing, Ned decides to stop being the King's Hand.
Before he can leave, he has a fight with Jaime Lannister that causes Robert and Cersei to ask him for explanations. With the already very tense atmosphere, Ned asks to Beric Dondarrion that finishes the Mountain - loyal knight to the Lannister - after learning that this one is attacking Earth of the Rivers and demands that Tywin appears in Landing of the king. If he does not, he will be considered a traitor. In doing so, Ned has broken the promise of a peaceful relationship with the Lannisters.
In the last hours of life of Robert Baratheon, this one tells to Ned that wants that he is regent until Joffrey reaches the age and orders him to write it in a letter; However, Ned omits the name of Joffrey and writes "the legitimate heir" since he had just discovered that he was not his biological son. It is then when it writes a letter to Stannis explaining its discoveries to him, but Cersei intercepts it.
Pinkie learns the situation and tries to convince him to take the opportunity to increase his own power. He suggests that he reign with Joffrey and, in case things get ugly, blackmail him with the truth about his ancestry. When Robert finally died, Cersei and Joffrey had been warned by Littleton that Ned would betray them, and so they had prepared their guards to capture him.
The only motivation that Little did to end Ned Stark was his love for Catelyn. Petyr Baelish grew up with the Tully children and fell in love with Catelyn as he grew up, but his love was never reciprocated.